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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Solving Problems, SM-Bank 019
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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\(\angle QST = 360-255 = 105^{\circ}\ \ \text{(360° about a point)}\)
\(\angle VSQ =70^{\circ} \ \ \text{(alternate angles)} \)
\(\angle VST\ =x^{\circ} \ \ \text{(alternate angles)} \)
| \(x^{\circ}\) | \(=105-70\) | |
| \(=35^{\circ}\) |
Show Worked Solution
\(\text{Add middle parallel line:}\)
\(\angle QST = 360-255 = 105^{\circ}\ \ \text{(360° about a point)}\)
\(\angle VSQ =70^{\circ} \ \ \text{(alternate angles)} \)
\(\angle VST\ =x^{\circ} \ \ \text{(alternate angles)} \)
| \(x^{\circ}\) | \(=105-70 \) | |
| \(=35^{\circ}\) |
Solving Problems, SM-Bank 018
In the diagram below, find the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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\(y^{\circ}\ =70^{\circ} \ \ \text{(alternate angles)} \)
\(x^{\circ}\ =z^{\circ} \ \ \text{(alternate angles)} \)
| \((z+y)^{\circ}\) | \(=110^{\circ}\ \) | |
| \((x+y)^{\circ}\) | \(=110^{\circ}\ \) | |
| \(x^{\circ}\) | \(=110-70\) | |
| \(=40^{\circ}\) |
Show Worked Solution
\(\text{Extend middle parallel line:}\)
\(y^{\circ}\ =70^{\circ} \ \ \text{(alternate angles)} \)
\(x^{\circ}\ =z^{\circ} \ \ \text{(alternate angles)} \)
| \((z+y)^{\circ}\) | \(=110^{\circ}\ \) | |
| \((x+y)^{\circ}\) | \(=110^{\circ}\ \) | |
| \(x^{\circ}\) | \(=110-70\) | |
| \(=40^{\circ}\) |
Solving Problems, SM-Bank 014
In the diagram below, find the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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\(\angle y^{\circ} = 40^{\circ}\ \ \text{(alternate angles)} \)
\(\angle x^{\circ}=360=40 = 320^{\circ}\ \ \text{(360° about a point)}\)
Show Worked Solution
\(\angle y^{\circ} = 40^{\circ}\ \ \text{(alternate angles)} \)
\(\angle x^{\circ}=360=40 = 320^{\circ}\ \ \text{(360° about a point)}\)
Solving Problems, SM-Bank 013
In the diagram below, find the value of \(a^{\circ}\), giving reasons for your answer. (2 marks)
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\(\angle b^{\circ} = 360-325 = 35^{\circ}\ \ \text{(360° about a point)} \)
\(\angle a^{\circ}=35^{\circ}\ \ \text{(alternate angles)}\)
Show Worked Solution
\(\angle b^{\circ} = 360-325 = 35^{\circ}\ \ \text{(360° about a point)} \)
\(\angle a^{\circ}=35^{\circ}\ \ \text{(alternate angles)}\)
Solving Problems, SM-Bank 012
In the diagram below, find the value of \(x^{\circ}\), giving reasons for your answer. (2 marks)
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\(\angle y^{\circ} = 180-(52+90) = 38^{\circ}\ \ \text{(180° in straight line)} \)
\(\angle x^{\circ}=38^{\circ}\ \ \text{(alternate angles)}\)
Show Worked Solution
\(\angle y^{\circ} = 180-(52+90) = 38^{\circ}\ \ \text{(180° in straight line)} \)
\(\angle x^{\circ}=38^{\circ}\ \ \text{(alternate angles)}\)
Solving Problems, SM-Bank 023
Find the value of \(x^{\circ}\) in the diagram, giving reasons for your answer. (3 marks)
Show Worked Solution
\(\text{Extend the middle parallel line:}\)
\(\text{Alternate angles are equal}\ (x^{\circ}) \).
\(\text{Cointerior angles sum to 180° (110° and 70°)}\)
\(x^{\circ} = 120-70=50^{\circ} \)
Solving Problems, SM-Bank 003
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^@` |
Solving Problems, SM-Bank 002
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^@` |
Solving Problems, SM-Bank 001
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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Show Worked Solution
`text(Alternate angles are equal)`
| `60` | `= x + 10` |
| `:.x` | `= 50^@` |