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.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.
- 2.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.
- 3.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.
- 4.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.
- 5.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.
- 6.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.
- 7.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.
- 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.Two straight lines cross at a point. Which statement about a pair of vertically opposite angles is always true?
- 10.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.
- 11.A regular polygon has an interior angle of 156°. Work out the number of sides of the polygon.
- 12.Two angles are complementary. One of them is 35°. Work out the size of the other angle.
- 13.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.
- 14.A regular nonagon has 9 sides. Work out the sum of its interior angles.
- 15.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.
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