Angles, polygons and properties of shapes – Year 10 GCSE maths test to download as PDF

Non-calculator. In triangle PQR, angle \(P=63^\circ\) and angle \(Q=57^\circ\). The side PR is extended to a point S beyond R.

1. Find angle \(PRQ\), giving a reason. (2 marks)
2. Find angle \(QRS\) and give a reason. (2 marks)

Calculator allowed.

1. Work out the interior angle of a regular 20-sided polygon. (2 marks)
2. A regular polygon has an exterior angle of \(18^\circ\). How many sides has it? (1 mark)
3. Work out the sum of the interior angles of a heptagon. (1 mark)

The angles of a quadrilateral are \(x\), \(2x+10\), \(3x-20\) and \(4x\) degrees.

1. Show that \(10x-10=360\). (2 marks)
2. Find the size of the largest angle. (2 marks)

A ship sails from port P on a bearing of \(072^\circ\) to port Q. It then sails on a bearing of \(144^\circ\) to port R. PQ = QR.

1. Find the back bearing of P from Q. (1 mark)
2. Find angle \(PQR\). (1 mark)
3. Find the bearing of R from P. (2 marks)

Higher tier. A, B and C are points on a circle with centre O. TA is a tangent. Angle \(ABC=64^\circ\).

1. Find angle \(AOC\) and give the reason. (2 marks)
2. Triangle OAC is isosceles. Find angle \(OAC\). (1 mark)
3. Find angle \(TAC\) given that TA is a tangent at A. (1 mark)