In the diagram below, find the value of \(x^{\circ}\), giving reasons for your answer. (3 marks)
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\(\text{Full interior angle}\ = 360-275=85^{\circ} \ \ \text{(360° about a point)} \)
\(\text{Since cointerior angles sum to 180°,}\)
\(\Rightarrow \text{interior angle (1)}\ = 180-125=55^{\circ} \)
\(\text{Since angles about a point sum to 360°,}\)
\(\Rightarrow \text{interior angle (2)}\ = 85-55=30^{\circ} \)
| \(x^{\circ}\) | \(=180-30\ \ \text{(cointerior angles)} \) | |
| \(=150^{\circ}\) |
\(\text{Add parallel line:}\)
\(\text{Full interior angle}\ = 360-275=85^{\circ} \ \ \text{(360° about a point)} \)
\(\text{Since cointerior angles sum to 180°,}\)
\(\Rightarrow \text{interior angle (1)}\ = 180-125=55^{\circ} \)
\(\text{Since angles about a point sum to 360°,}\)
\(\Rightarrow \text{interior angle (2)}\ = 85-55=30^{\circ} \)
| \(x^{\circ}\) | \(=180-30\ \ \text{(cointerior angles)} \) | |
| \(=150^{\circ}\) |