Higher June 2019 Unit 2 Q10
10. \(ABCD\) is a cyclic quadrilateral in a circle with centre \(O\).
\(A\hat{B}C\) = 126°.
Diagram not drawn to scale
Write down the size of each of the angles \(x\) and \(y\).
You must give a reason for each of your answers. [4]
\(x\) = …………… °
Reason: ……………………………………
\(y\) = …………… °
Reason: ……………………………………
| Scheme | Marks | Comments |
|---|---|---|
| x = 54(°) | B1 | |
| Opposite angles (of a) cyclic quad. (add up to 180°). | E1 | Dependent on an attempt at 180 – 126. |
| y = 108(°) | B1 | FT 2 × ‘their 54’ only if less than 360° |
| Angle at the centre (is twice the angle at the circumference). | E1 | Dependent on an attempt at 2 × ‘their 54’. |