4MA0 Higher January 2017 Paper 3 Q12
12
Diagram NOT accurately drawn
\(A\), \(B\), \(C\) and \(D\) are points on a circle with centre \(O\).
Angle \(ABC = 48^\circ\)
(a)
(i) Calculate the size of angle \(x\).
(ii) Give a reason for your answer. (2)
(b)
(i) Calculate the size of angle \(ADC\).
(ii) Give a reason for your answer. (2)
| Scheme | Marks |
|---|---|
| (i) 2 × 48 Answer: 96 | B1 |
| (ii) Answer: The angle at the centre is double the angle at the circumference | B1 |
| (2) |
Notes
B1: NB : accept twice, double, origin (\(O\))
accept ‘angle at circumference is half the angle at the centre’ oe
| Scheme | Marks |
|---|---|
| (i) 180 – 48 Answer: 132 | B1 |
| (ii) Answer: The opposite angles in a cyclic quadrilateral total 180° | B1 |
| (2) | |
| (4 marks) |
Notes
B1: accept supplementary angles
accept
The angle at the centre is double the angle at the circumference
with
angles at a point sum to 360°