Foundation June 2024 Unit 1 Q15
15. In the diagram below, ABC is a right-angled triangle and CDE is an isosceles triangle.
\(A\hat{B}C\) = 90°, \(B\hat{A}C\) = 64° 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(°) | A1 | |
| (\(y\) =) 26(°) | B1 | FT \(y\) = ‘their \(x\)’. |
| (\(z\) =) \(\dfrac{180 - 26}{2}\) | M1 | FT ‘their \(y\)’, provided \(y\) ≠ 90° or 60°. |
| = 77(°) | A1 |