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.
Angle facts, parallel lines and polygons worksheet — GCSE Foundation
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- 1.A regular polygon has an exterior angle of 45°. Work out the number of sides of the polygon.
- 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.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.
- 4.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.
- 5.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.
- 6.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.
- 7.A regular nonagon has 9 sides. Work out the sum of its interior angles.
- 8.Two angles are complementary. One of them is 35°. Work out the size of the other angle.
- 9.Which of these describes an obtuse angle?
- 10.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.
- 11.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.
- 12.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.
- 13.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.
- 14.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.
- 15.Two straight lines cross at a point. Which statement about a pair of vertically opposite angles is always true?
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