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 nonagon has 9 sides. Work out the sum of its interior angles.
- 2.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.
- 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.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.
- 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 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.
- 8.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.
- 9.Two straight lines cross at a point. Which statement about a pair of vertically opposite angles is always true?
- 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 regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.
- 12.An angle measures 108°. Write down the name given to an angle of this size.
- 13.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.
- 14.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.
- 15.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.
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