Angle facts, parallel lines and polygons worksheet — GCSE Foundation

1.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.

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

3.At a point on a straight line, two angles are formed. One of them is 63°. Work out the size of the other angle.

4.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.

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

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

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

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

9.A transversal crosses a pair of parallel lines. At one line, the angle is (5x + 4)°. The corresponding angle at the other line is (3x + 24)°. Work out the value of x.

10.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.

11.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.

12.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.

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

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

15.A straight line crosses a pair of parallel lines. At one of the crossing points, one of the four angles measures 55°. Work out the size of the angle next to it on a straight line at that crossing point.