Intermediate June 2024 Unit 1 Q4
4. In the diagram below, ABC is a right-angled triangle and CDE is an isosceles triangle.
\(A\hat{B}C = 90^\circ\), \(B\hat{A}C = 64^\circ\) and CD = CE.
AD and BE are straight lines intersecting at C.
Diagram not drawn to scale
Calculate the size of each of the angles \(x\), \(y\) and \(z\). [5]
\(x\) = ………… ° \(y\) = ………… ° \(z\) = ………… °
| Scheme | Marks | Comments |
|---|---|---|
| \((x = 180 -{}\ )\) 90 – 64 or equivalent | M1 | Check diagram for answers but answer line takes precedence. |
| = 26(\(^\circ\)) | A1 | |
| \((y =)\) 26(\(^\circ\)) | B1 | FT \(y\) = ‘their \(x\)’. |
| \((z =)\ \ \dfrac{180 - 26}{2}\) | M1 | FT ‘their \(y\)’, provided \(y \neq 90^\circ\) or \(60^\circ\). |
| = 77(\(^\circ\)) | A1 |