1MA0 Higher November 2016 Paper 2 Q18
*18
Diagram NOT accurately drawn
\(A\), \(B\), \(C\) and \(D\) are points on the circumference of a circle, centre \(O\).
\(BOD\) is a straight line.
Angle \(ACD = 62^\circ\)
Find the size of angle \(ADB\).
Give a reason for each stage in your working. (4)
| Answer | Mark | Notes |
|---|---|---|
| \(28^\circ\) | 4 | M1 for angle \(ABD = 62^\circ\) M1 for angle \(BAD = 90^\circ\) C2 for angle \(ADB = 28^\circ\) with full, appropriate reasons given angles in the same segment are equal; angles in a semicircle are 90°; angles in a triangle add up to 180° (C1 (dep on relevant M1) for one correct and appropriate reason relating to a circle theorem) OR M1 for angle \(AOD = 62^\circ \times 2\) (= 124°) M1 for \((180^\circ - 124^\circ) \div 2\) C2 for angle \(ADB = 28^\circ\) with full, appropriate reasons given the angle at the centre of a circle is twice the angle at the circumference; base angles of an isosceles triangle are equal; angles in a triangle add up to 180° (C1 (dep on relevant M1) for one correct and appropriate reason relating to a circle theorem) |