Angle facts, parallel lines and polygons worksheet — GCSE Foundation

1.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.

2.Which of these describes an obtuse angle?

3.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller 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.Two angles are complementary. One of them is 35°. Work out the size of the other angle.

6.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.

7.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.

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

9.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.

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

11.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.

12.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.

13.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.

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

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