Angle facts, parallel lines and polygons worksheet — GCSE Foundation

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

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 straight line crosses a pair of parallel lines. One of the co-interior (allied) angles is 118°. Work out the size of the other co-interior angle.

4.A conservatory has a roof panel shaped like a regular octagon. Work out the interior angle of the octagon, then use it to work out the size of the reflex angle at the same vertex, on the outside of the roof panel.

5.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.

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

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

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

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

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

12.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.

13.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.

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

15.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.