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
\(\text{Extend middle parallel line:}\)
\(y^{\circ}\ =70^{\circ} \ \ \text{(alternate angles)} \)
\(x^{\circ}\ =z^{\circ} \ \ \text{(alternate angles)} \)
| \((z+y)^{\circ}\) | \(=110^{\circ}\ \) | |
| \((x+y)^{\circ}\) | \(=110^{\circ}\ \) | |
| \(x^{\circ}\) | \(=110-70\) | |
| \(=40^{\circ}\) |