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.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°.
- 2.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.
- 3.In triangle ABC, angle A is 2x°, angle B is 3x° and angle C is 4x°. Work out the size of angle B.
- 4.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.
- 5.An angle measures 108°. Write down the name given to an angle of this size.
- 6.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.
- 7.A straight line crosses two parallel lines. One of the angles formed is (2x + 10)°, and the angle alternate to it is 74°. Work out the value of x.
- 8.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.
- 9.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.
- 10.At a point on a straight line, two angles are formed. One of them is 63°. Work out the size of the other angle.
- 11.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.
- 12.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.
- 13.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.
- 14.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.
- 15.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.
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