Angle facts, parallel lines and polygons worksheet — GCSE Foundation

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

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

3.Which of these describes an obtuse angle?

4.A straight line crosses two parallel lines. One of the angles formed is (2x + 10)°, and the angle alternate to it is 74°. Work out the value of x.

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

6.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.

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

8.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.

9.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.

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

11.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.

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

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

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

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.