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.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.

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

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

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

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

7.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.

8.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.

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

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

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

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

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.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.

15.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.