Determine the value of \(x^{\circ}\) in the quadrilateral above, giving reasons for your answer. (2 marks)
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Determine the value of \(x^{\circ}\) in the quadrilateral above, giving reasons for your answer. (2 marks)
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\(30^{\circ}\)
\(\text{Angle sum of quadrilaterals = 360°:} \)
\(360\) | \(=2x + 3x + 4x + 2x \) | |
\(12x^{\circ}\) | \(=360\) | |
\(x^{\circ}\) | \(=\dfrac{360}{12}\) | |
\(=30^{\circ}\) |
A pentagon is pictured below.
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i. \(540^{\circ}\)
ii. \(110^{\circ}\)
i. \(\text{Pentagon can be divided into 3 triangles (from one chosen vertex).}\)
\(\text{Sum of internal angles}\ = 3 \times 180 = 540^{\circ}\)
ii. \(540\) | \(=x + 2 \times 90 + 135+115 \) | |
\(540\) | \(=x+430\) | |
\(x^{\circ}\) | \(=540-430\) | |
\(=110^{\circ}\) |
Determine the value of the two unknown angles in the quadrilateral above, giving reasons for your answer. (3 marks)
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\(\text{Angle sum of quadrilaterals = 360°:} \)
\(360\) | \(=5x+3x+79+105 \) | |
\(8x\) | \(=360-184\) | |
\(x^{\circ}\) | \(=\dfrac{176}{8}\) | |
\(=22^{\circ}\) |
\(\text{Unknown angle 1}\ = 3 \times 22 = 66^{\circ}\)
\(\text{Unknown angle 2}\ = 5 \times 22 = 110^{\circ}\)
\(\text{Angle sum of quadrilaterals = 360°:} \)
\(360\) | \(=5x+3x+79+105 \) | |
\(8x\) | \(=360-184\) | |
\(x^{\circ}\) | \(=\dfrac{176}{8}\) | |
\(=22^{\circ}\) |
\(\text{Unknown angle 1}\ = 3 \times 22 = 66^{\circ}\)
\(\text{Unknown angle 2}\ = 5 \times 22 = 110^{\circ}\)
\(ABCD\) is a trapezium.
Determine the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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\(67^{\circ}\)
\(DA \parallel CB \ \ (ABCD\ \text{is a trapezium}) \)
\(x+113\) | \(=180\ \ \text{(cointerior angles)} \) | |
\(x^{\circ}\) | \(=180-113\) | |
\(=67^{\circ}\) |
\(ABCD\) is a trapezium.
Determine the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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\(83^{\circ}\)
\(AD \parallel BC \ \ (ABCD\ \text{is a trapezium}) \)
\(x+97\) | \(=180\ \ \text{(cointerior angles)} \) | |
\(x^{\circ}\) | \(=180-97\) | |
\(=83^{\circ}\) |
\(ABCD\) is a parallelogram.
Determine the value of \(a^{\circ}\), giving reasons for your answer. (2 marks)
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\(AB \parallel DC \ \ \text{(opposite sides of parallelogram)} \)
\(a+125\) | \(=180\ \ \text{(cointerior angles)} \) | |
\(a^{\circ}\) | \(=180-125\) | |
\(=55^{\circ}\) |
\(AB \parallel DC \ \ \text{(opposite sides of parallelogram)} \)
\(a+125\) | \(=180\ \ \text{(cointerior angles)} \) | |
\(a^{\circ}\) | \(=180-125\) | |
\(=55^{\circ}\) |
Find the value of \(a^{\circ}\) in the diagram below. (2 marks)
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\(132^{\circ}\)
\(\text{Since there are 360° in a quadrilateral:}\)
\(360\) | \(=a+62+85+81\) | |
\(360\) | \(=a+228\) | |
\(a^{\circ}\) | \(=360-228\) | |
\(=132^{\circ}\) |
Find the value of \(x^{\circ}\) in the diagram below. (2 marks)
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\(81^{\circ}\)
\(\text{Since there are 360° in a quadrilateral:}\)
\(360\) | \(=x+98+108+73\) | |
\(360\) | \(=x+279\) | |
\(x^{\circ}\) | \(=360-279\) | |
\(=81^{\circ}\) |
Find the value of \(a^{\circ}\) in the diagram below. (2 marks)
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\(60^{\circ}\)
\(\angle BCD\ \text{(reflex)} = 360-130=230^{\circ}\)
\(\text{Since there are 360° in a quadrilateral:}\)
\(360\) | \(=a+40+230+30\) | |
\(360\) | \(=a+300\) | |
\(a^{\circ}\) | \(=360-300\) | |
\(=60^{\circ}\) |
Find the value of \(x^{\circ}\) in the diagram below. (2 marks)
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\(110^{\circ}\)
\(\text{Since there are 360° in a quadrilateral:}\)
\(360\) | \(=x+55+105+90\) | |
\(360\) | \(=x+250\) | |
\(x^{\circ}\) | \(=360-250\) | |
\(=110^{\circ}\) |
The diagram of a quadrilateral is shown below.
Which name below does not refer to the quadrilateral in the diagram?
\(D\)
\(\text{Vertices need to be named in order (either clockwise or counter clockwise)}\)
\(CBDA\ \text{is not correct as vertex}\ B\ \text{and}\ D\ \text{are not adjacent.}\)
\(\Rightarrow D\)
\(ABCDE\) is a pentagon.
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i.
ii. \(ABCDE\ \text{can be divided into 3 triangles.}\)
\(\text{Angle sum of a triangle = 180°}\)
\(\text{Angle sum of}\ ABCDE = 3 \times 180^{\circ} = 540^{\circ}\)
i.
ii. \(ABCDE\ \text{can be divided into 3 triangles.}\)
\(\text{Angle sum of a triangle = 180°}\)
\(\text{Angle sum of}\ ABCDE = 3 \times 180^{\circ} = 540^{\circ}\)
Divide quadrilateral \(ABCD\) into triangles and using the angle sum of one triangle, determine the sum of the internal angles of a quadrilateral. (2 marks)
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\(ABCD\ \text{can be divided into 2 triangles.}\)
\(\text{Angle sum of a triangle = 180°}\)
\(\text{Angle sum of}\ ABCD = 2 \times 180^{\circ} = 360^{\circ}\)
\(ABCD\ \text{can be divided into 2 triangles.}\)
\(\text{Angle sum of a triangle = 180°}\)
\(\text{Angle sum of}\ ABCD = 2 \times 180^{\circ} = 360^{\circ}\)
Divide quadrilateral \(ABCD\) into triangles and using the angle sum of one triangle, determine the sum of the internal angles of a quadrilateral. (2 marks)
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\(ABCD\ \text{can be divided into 2 triangles.}\)
\(\text{Angle sum of a triangle = 180°}\)
\(\text{Angle sum of}\ ABCD = 2 \times 180^{\circ} = 360^{\circ}\)
\(ABCD\ \text{can be divided into 2 triangles.}\)
\(\text{Angle sum of a triangle = 180°}\)
\(\text{Angle sum of}\ ABCD = 2 \times 180^{\circ} = 360^{\circ}\)
Complete the table below by placing a tick or a cross in the appropriate box to indicate which properties belong to different quadrilaterals. (3 marks)
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Rhombus} & \textbf{Trapezium} & \textbf{Rectangle} \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals are perpendicular} \rule[-1ex]{0pt}{0pt} & & & \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are equal} \rule[-1ex]{0pt}{0pt} & & & \\
\hline
\rule{0pt}{2.5ex} \text{Adjacent sides are perpendicular} \rule[-1ex]{0pt}{0pt} & & & \\
\hline
\end{array}
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\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Rhombus} & \textbf{Trapezium} & \textbf{Rectangle} \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals are perpendicular} \rule[-1ex]{0pt}{0pt} & \checkmark & \cross & \cross \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are equal} \rule[-1ex]{0pt}{0pt} & \checkmark & \cross & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Adjacent sides are perpendicular} \rule[-1ex]{0pt}{0pt} & \cross & \cross & \checkmark \\
\hline
\end{array}
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Rhombus} & \textbf{Trapezium} & \textbf{Rectangle} \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals are perpendicular} \rule[-1ex]{0pt}{0pt} & \checkmark & \cross & \cross \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are equal} \rule[-1ex]{0pt}{0pt} & \checkmark & \cross & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Adjacent sides are perpendicular} \rule[-1ex]{0pt}{0pt} & \cross & \cross & \checkmark \\
\hline
\end{array}
Complete the table below by placing a tick or a cross in the appropriate box to indicate which properties belong to different quadrilaterals. (3 marks)
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Square} & \textbf{Kite} & \textbf{Parallelogram} \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are parallel} \rule[-1ex]{0pt}{0pt} & & & \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals bisect each other} \rule[-1ex]{0pt}{0pt} & & & \\
\hline
\rule{0pt}{2.5ex} \text{Two pairs of equal adjacent sides} \rule[-1ex]{0pt}{0pt} & & & \\
\hline
\end{array}
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\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Square} & \textbf{Kite} & \textbf{Parallelogram} \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are parallel} \rule[-1ex]{0pt}{0pt} & \checkmark & \cross & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals bisect each other} \rule[-1ex]{0pt}{0pt} & \checkmark & \cross & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Two pairs of equal adjacent sides} \rule[-1ex]{0pt}{0pt} & \checkmark & \checkmark & \cross \\
\hline
\end{array}
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Square} & \textbf{Kite} & \textbf{Parallelogram} \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are parallel} \rule[-1ex]{0pt}{0pt} & \checkmark & \cross & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals bisect each other} \rule[-1ex]{0pt}{0pt} & \checkmark & \cross & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Two pairs of equal adjacent sides} \rule[-1ex]{0pt}{0pt} & \checkmark & \checkmark & \cross \\
\hline
\end{array}
Complete the table below by placing a tick or a cross in the appropriate box to indicate which properties belong to different quadrilaterals. (3 marks)
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Trapezium} & \textbf{Rectangle} & \textbf{Rhombus} \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are parallel} \rule[-1ex]{0pt}{0pt} & & & \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals are perpendicular} \rule[-1ex]{0pt}{0pt} & & & \\
\hline
\rule{0pt}{2.5ex} \text{Adjacent sides are perpendicular} \rule[-1ex]{0pt}{0pt} & & & \\
\hline
\end{array}
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\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Trapezium} & \textbf{Rectangle} & \textbf{Rhombus} \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are parallel} \rule[-1ex]{0pt}{0pt} & \cross & \checkmark & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals are perpendicular} \rule[-1ex]{0pt}{0pt} & \cross & \cross & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Adjacent sides are perpendicular} \rule[-1ex]{0pt}{0pt} & \cross & \checkmark & \cross \\
\hline
\end{array}
\begin{array} {|l|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ \ \ \ \ \textbf{Property} \rule[-1ex]{0pt}{0pt} & \textbf{Trapezium} & \textbf{Rectangle} & \textbf{Rhombus} \\
\hline
\rule{0pt}{2.5ex} \text{Opposite sides are parallel} \rule[-1ex]{0pt}{0pt} & \cross & \checkmark & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Diagonals are perpendicular} \rule[-1ex]{0pt}{0pt} & \cross & \cross & \checkmark \\
\hline
\rule{0pt}{2.5ex} \text{Adjacent sides are perpendicular} \rule[-1ex]{0pt}{0pt} & \cross & \checkmark & \cross \\
\hline
\end{array}
Determine the value of \(a^{\circ}\), \(b^{\circ}\), and \(c^{\circ}\), giving reasons for your answer. (3 marks)
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\(\text{All radii are equal (see diagram).}\)
\(a^{\circ} = 70^{\circ}\ \ \text{(angles opposite equal sides in isosceles triangle)} \)
\(b^{\circ} = 2 \times 70 = 140^{\circ}\ \ \text{(external angle = sum of interior opposite angles)} \)
\(140^{\circ} + 2 \times c^{\circ}\) | \(=180^{\circ}\ \ \text{(angle sum of isosceles triangle)} \) | |
\(2c^{\circ}\) | \(=180-40\) | |
\(c^{\circ}\) | \(=\dfrac{40}{2} = 20^{\circ} \) |
\(\text{All radii are equal (see diagram).}\)
\(a^{\circ} = 70^{\circ}\ \ \text{(angles opposite equal sides in isosceles triangle)} \)
\(b^{\circ} = 2 \times 70 = 140^{\circ}\ \ \text{(external angle = sum of interior opposite angles)} \)
\(140^{\circ} + 2 \times c^{\circ}\) | \(=180^{\circ}\ \ \text{(angle sum of isosceles triangle)} \) | |
\(2c^{\circ}\) | \(=180-40\) | |
\(c^{\circ}\) | \(=\dfrac{40}{2} = 20^{\circ} \) |
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a.
\(\text{All radii are equal (see diagram).}\)
\(\text{Isosceles triangle}\ \ \Rightarrow\ \ \text{angles opposite equal sides are equal}\)
\(a^{\circ} = 180-(2 \times 60)=60^{\circ}\ \ \text{(angle sum of triangle)} \)
b. \(c^{\circ} = 180-60=120^{\circ}\ \ \text{(180° in straight line)} \)
\(120^{\circ}\) | \(=85\ \ \text{(external angle = sum of interior opposite angles)} \) | |
\(a^{\circ}\) | \(= \dfrac{85}{2}\) | |
\(=42.5^{\circ}\) |
a.
\(\text{All radii are equal (see diagram).}\)
\(\text{Isosceles triangle}\ \ \Rightarrow\ \ \text{angles opposite equal sides are equal}\)
\(a^{\circ} = 180-(2 \times 60)=60^{\circ}\ \ \text{(angle sum of triangle)} \)
b. \(c^{\circ} = 180-60=120^{\circ}\ \ \text{(180° in straight line)} \)
\(120^{\circ}\) | \(=85\ \ \text{(external angle = sum of interior opposite angles)} \) | |
\(a^{\circ}\) | \(= \dfrac{85}{2}\) | |
\(=42.5^{\circ}\) |
An isosceles triangle is pictured below.
Determine the value of \(a^{\circ}\), giving reasons for your answer. (2 marks)
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\(b^{\circ} = 180-95=85^{\circ}\ \ \text{(180° in straight line)} \)
\(\text{Isosceles triangle}\ \ \Rightarrow\ \ \text{angles opposite equal sides are equal}\)
\(2a^{\circ}\) | \(=85\ \ \text{(external angle = sum of interior opposite angles)} \) | |
\(a^{\circ}\) | \(= \dfrac{85}{2}\) | |
\(=42.5^{\circ}\) |
\(b^{\circ} = 180-95=85^{\circ}\ \ \text{(180° in straight line)} \)
\(\text{Isosceles triangle}\ \ \Rightarrow\ \ \text{angles opposite equal sides are equal}\)
\(2a^{\circ}\) | \(=85\ \ \text{(external angle = sum of interior opposite angles)} \) | |
\(a^{\circ}\) | \(= \dfrac{85}{2}\) | |
\(=42.5^{\circ}\) |
Find the value of \(a^{\circ}\), giving reasons for your answer. (2 marks)
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\(a^{\circ}+67^{\circ}\) | \(=108\ \ \text{(external angle = sum of interior opposite angles)} \) | |
\(a^{\circ}\) | \(= 108-67\) | |
\(=41^{\circ}\) |
\(a^{\circ}+67^{\circ}\) | \(=108\ \ \text{(external angle = sum of interior opposite angles)} \) | |
\(a^{\circ}\) | \(= 108-67\) | |
\(=41^{\circ}\) |
The diagram below shows an isosceles triangle.
Find the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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\(2y^{\circ}\) | \(=180-32\ \ \text{(angles opposite equal sides in isosceles triangle)} \) | |
\(y^{\circ}\) | \(=\dfrac{148}{2}\) | |
\(=74^{\circ}\) | ||
\(x^{\circ}\) | \(=32+74\ \ \text{(external angle = sum of interior opposite angles)} \) | |
\(=106^{\circ}\) |
\(2y^{\circ}\) | \(=180-32\ \ \text{(angles opposite equal sides in isosceles triangle)} \) | |
\(y^{\circ}\) | \(=\dfrac{148}{2}\) | |
\(=74^{\circ}\) | ||
\(x^{\circ}\) | \(=32+74\ \ \text{(external angle = sum of interior opposite angles)} \) | |
\(=106^{\circ}\) |
Find the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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\(2y^{\circ}\) | \(=180-78\ \ \text{(angles opposite equal sides in isosceles triangle)} \) | |
\(y^{\circ}\) | \(=\dfrac{102}{2}\) | |
\(=51^{\circ}\) | ||
\(x^{\circ}\) | \(=78+51\ \ \text{(external angle = sum of interior opposite angles)} \) | |
\(=129^{\circ}\) |
\(2y^{\circ}\) | \(=180-78\ \ \text{(angles opposite equal sides in isosceles triangle)} \) | |
\(y^{\circ}\) | \(=\dfrac{102}{2}\) | |
\(=51^{\circ}\) | ||
\(x^{\circ}\) | \(=78+51\ \ \text{(external angle = sum of interior opposite angles)} \) | |
\(=129^{\circ}\) |
Find the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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\(26^{\circ}\)
\(x^{\circ}+54^{\circ}\) | \(=80\ \ \text{(external angle = sum of interior opposite angles)} \) | |
\(x^{\circ}\) | \(=80-54\) | |
\(=26^{\circ}\) |
Find the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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\(115^{\circ}\)
\(x^{\circ}\) | \(=57+58\ \ \text{(external angle = sum of interior opposite angles)} \) | |
\(=115^{\circ}\) |
In the diagram, \(AB\) is parallel to \(DE\).
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a.
b. \(DE\ \text{is a straight line.}\)
\(a^{\circ} + b^{\circ} + c^{\circ} = 180^{\circ}\ \ \text{(180° in a straight line)}\)
\(\therefore \ \text{Angle sum of}\ \Delta = a^{\circ} + b^{\circ} + c^{\circ} = 180^{\circ}\)
a.
b. \(DE\ \text{is a straight line.}\)
\(a^{\circ} + b^{\circ} + c^{\circ} = 180^{\circ}\ \ \text{(180° in a straight line)}\)
\(\therefore \ \text{Angle sum of}\ \Delta = a^{\circ} + b^{\circ} + c^{\circ} = 180^{\circ}\)
The diagram below shows a right-angled triangle.
Determine the value of \(a^{\circ}\), giving reasons for your answer. (2 marks)
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\(138^{\circ}\)
\(\text{Right angle}\ = 90^{\circ} \)
\(a^{\circ}\) | \(=48+90\ \ \text{(external angle = sum of interior opposite angles)} \) | |
\(=138^{\circ}\) |
The diagram below shows an isosceles triangle.
Determine the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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\(40^{\circ}\)
\(\text{Isosceles triangle}\ \ \Rightarrow\ \ \text{angles opposite equal sides are equal}\)
\(x^{\circ}\) | \(=180-(2 \times 70)\ \ \text{(180° in triangle)} \) | |
\(=180-140\) | ||
\(=40^{\circ}\) |
The diagram below shows an isosceles triangle.
Determine the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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\(110^{\circ}\)
\(\text{Isosceles triangle}\ \ \Rightarrow\ \ \text{angles opposite equal sides are equal}\)
\(x^{\circ}\) | \(=180-(2 \times 35)\ \ \text{(180° in triangle)} \) | |
\(=110^{\circ}\) |
The diagram below shows an isosceles triangle.
Determine the value of \(a^{\circ}\), giving reasons for your answer. (2 marks)
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\(71^{\circ}\)
\(\text{Isosceles triangle}\ \ \Rightarrow\ \ \text{angles opposite equal sides are equal}\)
\(2a^{\circ}\) | \(=180-38\ \ \text{(180° in triangle)} \) | |
\(a^{\circ}\) | \(=\dfrac{142}{2}\) | |
\(=71^{\circ}\) |
The diagram below shows an isosceles triangle.
Determine the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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\(59^{\circ}\)
\(\text{Isosceles triangle}\ \ \Rightarrow\ \ \text{angles opposite equal sides are equal}\)
\(2x^{\circ}\) | \(=180-62\ \ \text{(180° in triangle)} \) | |
\(x^{\circ}\) | \(=\dfrac{118}{2}\) | |
\(=59^{\circ}\) |
In the right-angled triangle below, determine the value of \(x^{\circ}\). (2 marks)
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\(57^{\circ}\)
\(\text{Right-angle}\ = 90^{\circ}\)
\(x^{\circ}\) | \(=180-(90+72)\ \ \text{(180° in triangle)} \) | |
\(=18^{\circ}\) |
In the right-angled triangle below, determine the value of \(x^{\circ}\). (2 marks)
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\(57^{\circ}\)
\(\text{Right-angle}\ = 90^{\circ}\)
\(x^{\circ}\) | \(=180-(90+33)\ \ \text{(180° in triangle)} \) | |
\(=57^{\circ}\) |
A six sided figure is drawn below.
What is the sum of the six interior angles? (2 marks)
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`720^@`
`text(Reflex angle) = 360-90 = 270^@`
`:.\ text(Sum of interior angles)`
`= (270 xx 2) + (30 xx 2) + (60 xx 2)`
`= 720^@`
What is the size of the angle marked \(x^{\circ}\) in this diagram? (2 marks)
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\(110^{\circ}\)
In the diagram \(AB\) is a straight line.
Calculate the size of the angle marked \(x^{\circ}\), giving reasons for your answer. (3 marks)
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Pablo creates a design that is made up of 3 rectangles and 2 straight lines, as shown below.
What is the size of angle \(x^{\circ}\)? (3 marks)
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\(\text{135 degrees}\)
A triangle is divided into 2 parts by a straight line.
The angles are then labelled.
Which statement is true about the sum of angles?
`C`
`text(Consider each option:)`
`text(Option A:)\ \ b + c + d != 180\ \ => \ b+c = 180^@`
`text(Option B:)\ \ c + d + e != 360^@\ \ => \ c + d + e = 180^@\ \ text{(angle sum of triangle)}`
`text(Option C:)\ \ a + b + f + g = 360^@`
`=>\ text(Correct since the angle sum of a quadrilateral = 360°)`
`text(Option D:)\ \ d + e + f + g != 180\ \ => \ e + f = 180^@`
`=> C`
Tom drew this shape on grid paper.
Which one of the shapes below when joined to Tom's shape without an overlap, will not make isosceles triangle?
A. | |
B. | |
C. | |
D. | |
\(C\)
\(\text{An isosceles triangle has two sides of the same length.}\)
\(\text{Option C will form a scalene triangle (all sides different lengths).}\)
\(\Rightarrow C\)
Which statement about the triangle pictured above is correct?
`C`
`text(The third angle of the triangle)\ = 180-(60+60) = 60°`
`:.\ text(It is an equilateral triangle.)`
`=>C`
\(D\)
Which statement is always true?
`D`
`text{Consider each option:}`
`A:\ \text{Isosceles (not scalene) have two equal angles.}`
`B:\ \text{Only opposite angles in a parallelogram are equal.}`
`C:\ \text{At least one pair of opposite sides of a trapezium are not equal.}`
`D:\ \text{Rhombuses have perpendicular diagonals.}`
`=>D`
Which of these are always equal in length?
`C`
`PQRS` is a parallelogram.
Which of these must be a property of `PQRS`?
`D`
`text{By elimination:}`
`A\ \text{and}\ B\ \text{clearly incorrect.}`
`C\ \text{true if all sides are equal (rhombus) but not true for all parallelograms.}`
`text(Line)\ PS\ text(must be parallel to line)\ QR.`
`=>D`
A closed shape has two pairs of equal adjacent sides.
What is the shape?
`C`
`text(Kite.)`
`text{(Note that a rectangle has a pair of equal opposite sides)}`
`=>C`
Which one of the following triangles is impossible to draw?
`D`
`text(A right angle = 90°.)`
`text{Since an obtuse angle is greater than 90°, it is impossible for}`
`text(a triangle, with an angle sum less than 180°, to have both.)`
`=>D`
A triangle has two acute angles.
What type of angle couldn't the third angle be?
`D`
`text(A triangle’s angles add up to 180°, and a reflex angle is)`
`text(greater than 180°.)`
`:.\ text(The third angle cannot be reflex.)`
`=>D`