Angle facts, parallel lines and polygons worksheet — GCSE Foundation

1.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.

2.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.

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

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

6.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.

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

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

9.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.

10.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.

11.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.

12.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.

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

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

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