Find the value of \(x^{\circ}\) in the diagram, giving reasons for your answer. (3 marks)
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\(\text{Extend the parallel line on the left:}\)
\(\text{Angle opposite}\ \angle ABC = 3x^{\circ}\ \ \text{(vertically opposite)}\)
\(\angle DEB = 360-(90+135) = 135^{\circ}\ \ \text{(360° about a point)} \)
| \(3x+135\) | \(=180\ \ \text{(cointerior angles)} \) | |
| \(3x\) | \(=180-135\) | |
| \(x^{\circ}\) | \(=\dfrac{45}{3}\) | |
| \(=15^{\circ}\) |