Angle facts, parallel lines and polygons worksheet — GCSE Foundation

1.A roof truss has two horizontal parallel rafters, one above the other. A straight strut crosses both rafters. Where the strut crosses the lower rafter, the angle above the rafter and to the left of the strut is 65°. Work out the size of the angle above the upper rafter and to the right of the strut, where the strut crosses it.

2.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.

3.Freya is designing a triangular flower bed. Two of its corners have equal angles, and the angle at the third corner is 40°. Work out the size of one of the two equal corner angles.

4.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.

5.A regular polygon has an exterior angle of 45°. Work out the number of sides of the polygon.

6.Two straight lines cross at a point. Which statement about a pair of vertically opposite angles is always true?

7.A ramp's sloped surface crosses two horizontal parallel rails. At the top rail, the angle between the ramp and the rail on the right of the ramp is (3x + 10)°. At the bottom rail, the angle between the ramp and the rail on the left of the ramp is (5x − 30)°. Work out the value of x.

8.The interior angles of a pentagon are 100°, 110°, 120°, x° and x°. Work out the size of each of the two angles marked x°.

9.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.

10.A straight line crosses two parallel lines. An angle of 65° is formed at one crossing. At the other crossing, the angle that lies between the two parallel lines on the opposite side of the crossing line is also 65°. Write down the angle fact that explains why these two angles are equal.

11.A regular nonagon has 9 sides. Work out the sum of its interior angles.

12.An angle measures 108°. Write down the name given to an angle of this size.

13.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.

14.In triangle ABC the angle at A and the angle at C are equal. The side AB is extended beyond B, and the exterior angle formed at B measures 98°. Work out the size of the angle at A.

15.A regular hexagon is divided into six identical triangles by joining its centre to each of the six vertices. Work out the size of the angle of one of these triangles at the centre of the hexagon.