Angle facts, parallel lines and polygons worksheet — GCSE Foundation

1.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.

2.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.

3.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.

4.Which of these describes an obtuse angle?

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

6.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.

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

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

9.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.

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

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

12.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.

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

15.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.