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
\(\text{Add middle parallel line:}\)
\(\angle QST = 360-255 = 105^{\circ}\ \ \text{(360° about a point)}\)
\(\angle VSQ =70^{\circ} \ \ \text{(alternate angles)} \)
\(\angle VST\ =x^{\circ} \ \ \text{(alternate angles)} \)
| \(x^{\circ}\) | \(=105-70 \) | |
| \(=35^{\circ}\) |