Aussie Maths & Science Teachers: Save your time with SmarterEd
What is the value of \(x^{\circ}\) in this diagram? (2 marks)
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\(\text{Adjacent angle to 144°}\ = 180-144=36^{\circ}\ \ \text{(180° in straight line)}\)
\(x^{\circ}= 180-(90 + 36)=54^{\circ}\ \ \text{(180° in straight line)}\)
In the diagram below, \(DG\) is parallel to \(BC\), and \(\angle ABC = 115^{\circ} \).
Find the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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In the diagram below, \(BE\) is parallel to \(CD\), and \(\angle ABE = 160^{\circ} \).
Find the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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In the diagram below, \(QR\) is parallel to \(SU\).
Find the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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In the diagram below, \(PR\) is parallel to \(TU\) and reflex \(\angle QST = 255^{\circ}\)
Find the value of \(x^{\circ}\), giving reasons for your answer. (3 marks)
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\(\angle QST = 360-255 = 105^{\circ}\ \ \text{(360° about a point)}\)
\(\angle VSQ =70^{\circ} \ \ \text{(alternate angles)} \)
\(\angle VST\ =x^{\circ} \ \ \text{(alternate angles)} \)
| \(x^{\circ}\) | \(=105-70\) | |
| \(=35^{\circ}\) |
\(\text{Add middle parallel line:}\)
\(\angle QST = 360-255 = 105^{\circ}\ \ \text{(360° about a point)}\)
\(\angle VSQ =70^{\circ} \ \ \text{(alternate angles)} \)
\(\angle VST\ =x^{\circ} \ \ \text{(alternate angles)} \)
| \(x^{\circ}\) | \(=105-70 \) | |
| \(=35^{\circ}\) |
In the diagram below, find the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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\(y^{\circ}\ =70^{\circ} \ \ \text{(alternate angles)} \)
\(x^{\circ}\ =z^{\circ} \ \ \text{(alternate angles)} \)
| \((z+y)^{\circ}\) | \(=110^{\circ}\ \) | |
| \((x+y)^{\circ}\) | \(=110^{\circ}\ \) | |
| \(x^{\circ}\) | \(=110-70\) | |
| \(=40^{\circ}\) |
\(\text{Extend middle parallel line:}\)
\(y^{\circ}\ =70^{\circ} \ \ \text{(alternate angles)} \)
\(x^{\circ}\ =z^{\circ} \ \ \text{(alternate angles)} \)
| \((z+y)^{\circ}\) | \(=110^{\circ}\ \) | |
| \((x+y)^{\circ}\) | \(=110^{\circ}\ \) | |
| \(x^{\circ}\) | \(=110-70\) | |
| \(=40^{\circ}\) |
In the diagram below, find the value of \(x^{\circ}\), giving reasons for your answer. (3 marks)
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\(\text{Full interior angle}\ = 360-275=85^{\circ} \ \ \text{(360° about a point)} \)
\(\text{Since cointerior angles sum to 180°,}\)
\(\Rightarrow \text{interior angle (1)}\ = 180-125=55^{\circ} \)
\(\text{Since angles about a point sum to 360°,}\)
\(\Rightarrow \text{interior angle (2)}\ = 85-55=30^{\circ} \)
| \(x^{\circ}\) | \(=180-30\ \ \text{(cointerior angles)} \) | |
| \(=150^{\circ}\) |
\(\text{Add parallel line:}\)
\(\text{Full interior angle}\ = 360-275=85^{\circ} \ \ \text{(360° about a point)} \)
\(\text{Since cointerior angles sum to 180°,}\)
\(\Rightarrow \text{interior angle (1)}\ = 180-125=55^{\circ} \)
\(\text{Since angles about a point sum to 360°,}\)
\(\Rightarrow \text{interior angle (2)}\ = 85-55=30^{\circ} \)
| \(x^{\circ}\) | \(=180-30\ \ \text{(cointerior angles)} \) | |
| \(=150^{\circ}\) |
In the diagram below, find the value of \(a^{\circ}\), giving reasons for your answer. (2 marks)
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In the diagram below, find the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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In the diagram below, find the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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\(\angle y^{\circ} = 40^{\circ}\ \ \text{(alternate angles)} \)
\(\angle x^{\circ}=360=40 = 320^{\circ}\ \ \text{(360° about a point)}\)
\(\angle y^{\circ} = 40^{\circ}\ \ \text{(alternate angles)} \)
\(\angle x^{\circ}=360=40 = 320^{\circ}\ \ \text{(360° about a point)}\)
In the diagram below, find the value of \(a^{\circ}\), giving reasons for your answer. (2 marks)
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\(\angle b^{\circ} = 360-325 = 35^{\circ}\ \ \text{(360° about a point)} \)
\(\angle a^{\circ}=35^{\circ}\ \ \text{(alternate angles)}\)
\(\angle b^{\circ} = 360-325 = 35^{\circ}\ \ \text{(360° about a point)} \)
\(\angle a^{\circ}=35^{\circ}\ \ \text{(alternate angles)}\)
In the diagram below, find the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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\(\angle y^{\circ} = 180-(52+90) = 38^{\circ}\ \ \text{(180° in straight line)} \)
\(\angle x^{\circ}=38^{\circ}\ \ \text{(alternate angles)}\)
\(\angle y^{\circ} = 180-(52+90) = 38^{\circ}\ \ \text{(180° in straight line)} \)
\(\angle x^{\circ}=38^{\circ}\ \ \text{(alternate angles)}\)
In the diagram below, \(QR\) is parallel to lines \(SU\) and \(VW\).
Find the value of \(x^{\circ}\), giving reasons for your answer. (3 marks)
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In the diagram below, \(BC\) is parallel to \(DE\) and \(\angle ACB\) is a right-angle.
Find the value of \(x^{\circ}\), giving reasons for your answer. (3 marks)
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\(\text{Extend line}\ BC: \)
\(\angle GCF=180-120=60^{\circ}\ \ \text{(180° in a straight line)}\)
\(x^{\circ} = 60^{\circ} \ \ \text{(corresponding angles)}\)
\(\text{Extend line}\ BC: \)
\(\angle GCF=180-120=60^{\circ}\ \ \text{(180° in a straight line)}\)
\(x^{\circ} = 60^{\circ} \ \ \text{(corresponding angles)}\)
In the diagram below, two parallel lines \(OB\) and \(DC\) cut the horizontal transversal \(OE\), and \(OA\) is perpendicular to \(OE\).
Find the value of \(a^{\circ}\), giving reasons for your answer. (2 marks)
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Determine if two lines in the diagram below are parallel, giving reasons for your answer. (2 marks)
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Find the value of \(x^{\circ}\) in the diagram below, giving reasons for your answer. (2 marks)
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Find the value of \(x^{\circ}\) in the diagram, giving reasons for your answer. (2 marks)
Find the value of \(x^{\circ}\) in the diagram, giving reasons for your answer. (2 marks)
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\(\text{Angle above}\ \angle (3x)^{\circ} = (180-3x)^{\circ}\ \ \text{(180° in a straight line)}\)
| \(180-3x\) | \(=x\ \ \text{(corresponding angles)} \) | |
| \(4x\) | \(=180\) | |
| \(x^{\circ}\) | \(=\dfrac{180}{4}\) | |
| \(=45^{\circ}\) |
Find the value of \(x^{\circ}\) in the diagram, giving reasons for your answer. (3 marks)
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\(\text{Extend the parallel line on the left:}\)
\(\text{Angle opposite}\ \angle ABC = 3x^{\circ}\ \ \text{(vertically opposite)}\)
\(\angle DEB = 360-(90+135) = 135^{\circ}\ \ \text{(360° about a point)} \)
| \(3x+135\) | \(=180\ \ \text{(cointerior angles)} \) | |
| \(3x\) | \(=180-135\) | |
| \(x^{\circ}\) | \(=\dfrac{45}{3}\) | |
| \(=15^{\circ}\) |
Find the value of \(x^{\circ}\) in the diagram, giving reasons for your answer. (2 marks)
Find the value of \(x\) in the diagram, giving reasons for your answer. (2 marks)
\(\text{Supplementary angles sum to 180°}\ (180-82 = 98^{\circ}) \)
| \(x-15\) | \(=98\ \ \text{(corresponding angles)}\) | |
| \(x^{\circ}\) | \(=98+15\) | |
| \(=113^{\circ}\) |
Find the value of \(x^{\circ}\) in the diagram, giving reasons for your answer. (3 marks)
\(\text{Extend the middle parallel line:}\)
\(\text{Alternate angles are equal}\ (x^{\circ}) \).
\(\text{Cointerior angles sum to 180° (110° and 70°)}\)
\(x^{\circ} = 120-70=50^{\circ} \)
A clock displayed the time ten o'clock, as shown on the diagram below.
The angle, `x^{\circ}`, between the small hand and the large hand is
A clock displayed the time four o'clock, as shown on the diagram below.
Calculate the angle, `x^{\circ}`, between the small hand and the large hand. (2 marks)
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A clock displayed the time one o'clock, as shown on the diagram below.
The angle, `theta`, between the small hand and the large hand is
How many degrees does the minute hand of a clock turn in 35 minutes? (2 marks)
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How many degrees does the hour hand of a clock turn in 60 minutes? (2 marks)
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In the figure below, the lines `p` and `q` are parallel.
Determine the value of `x^@`. (3 marks)
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| `x^@` | `= 75 + 35` |
| `= 110^@` |
In the figure below, the lines `G` and `F` are parallel.
Determine the value of `x^@`. (3 marks)
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| `x^@` | `= 108-67` |
| `= 41^@` |
Two boats leave from Fremantle. One sails to the Wharf at Rottnest Island and the other sails to Cervantes.
The direction each boat sailed is shown in the map below.
Determine the value of `x°` on the map. (2 marks)
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`text(Alternate angles are equal)`
| `60` | `= x + 10` |
| `:.x` | `= 50^@` |