Higher June 2019 Paper 5 Q16
16 A, B, C and D are points on the circumference of a circle, centre O.
Angle BAD = 112° and angle DCO = 33°.
Not to scale
(a) Show that angle \(y = 35\)°.
Give reasons for each stage of your working. [4]
Give reasons for each stage of your working. [4]
(b) Work out angle \(z\).
Give reasons for your answer.
Give reasons for your answer.
Angle \(z\) = ......... ° because ...... [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [Angle DCB =] 180 – 112 | M1 | Must show the subtraction | Must not be associated with wrong angle |
| [Opposite angles in a] cyclic quadrilateral [are supplementary] oe | M1 | Do not accept any incorrect statement e.g. opposite angles in a cyclic quad are equal, angles of a cyclic quad = 180. Condone issues with spelling provided clear | |
| [Angle BCO =] 68 – 33 = 35 | M1 | Must show the subtraction | Must not be associated with wrong angle If [angle BCO =] 180 – 112 – 33 is shown this implies first M1 and third M1 |
| \(y = 35\) and [triangle BOC =] isosceles with no incorrect statement | M1 | For M1 must mention isosceles with \(y = 35\) stated not just shown on the diagram | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 55 Angles in triangle [BOC sum to 180] oe | B1 M1 | Accept [triangle BOC = ] isosceles | Accept triangle and 180 without ‘angle’ |
| Angle at circumference is half angle at centre oe | M1 | Must use correct terminology, angle, circumference, half oe (or double oe), centre. Accept arc for circumference If more than 2 reasons given then treat each extra reason as choice | |