Angle facts, parallel lines and polygons worksheet — GCSE Foundation

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

2.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.

3.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.

4.Two identical ladders lean against the same vertical wall from opposite sides, each making an angle of 58.2° with the ground. The two ladders and the ground form a triangle. Work out the size of the angle between the two ladders at the top, where they meet.

5.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.

6.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.

7.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.

8.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.

9.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.

10.In triangle ABC, angle A is 2x°, angle B is 3x° and angle C is 4x°. Work out the size of angle B.

11.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.

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

13.Two angles are complementary. One of them is 35°. Work out the size of the other angle.

14.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°.

15.A straight transversal crosses a pair of parallel lines. At one crossing point, the angle between the transversal and a parallel line is 118°. Work out the size of the co-interior (allied) angle at the other crossing point.