Printable · GCSE Foundation · ages 14-16
Angle facts, parallel lines and polygons worksheet — GCSE Foundation
Fifteen questions on "angle facts, parallel lines and polygons" — DfE statement G3. Print it, or print three versions so neighbours cannot copy by letter; the key gives the letter for each version.
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Angle facts, parallel lines and polygons worksheet — GCSE Foundation
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- 1.Two straight lines cross at a point. Which statement about a pair of vertically opposite angles is always true?
- 2.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.
- 3.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.
- 4.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.
- 5.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.
- 6.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.
- 7.An angle measures 108°. Write down the name given to an angle of this size.
- 8.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.
- 9.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.
- 10.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.
- 11.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.
- 12.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.
- 13.At a point on a straight line, two angles are formed. One of them is 63°. Work out the size of the other angle.
- 14.The interior angles of a pentagon are 100°, 110°, 120°, x° and x°. Work out the size of each of the two angles marked x°.
- 15.A regular nonagon has 9 sides. Work out the sum of its interior angles.
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