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

Maths · GCSE Foundation · G3 · Angle facts, parallel lines and polygons · 15 questions

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1.Two angles are complementary. One of them is 35°. Work out the size of the other angle.
(a)90°
(b)55°
(c)145°
(d)325°
2.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.
(a)−32
(b)48
(c)32
(d)37
3.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.
(a)Co-interior angles add up to 180°
(b)Angles on a straight line add up to 180°
(c)Corresponding angles are equal
(d)Alternate angles are equal
4.In triangle ABC, angle A is 2x°, angle B is 3x° and angle C is 4x°. Work out the size of angle B.
(a)60°
(b)20°
(c)120°
(d)80°
5.A regular polygon has an exterior angle of 45°. Work out the number of sides of the polygon.
(a)4
(b)45
(c)8
(d)315
6.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.
(a)121.8
(b)58.2
(c)116.4
(d)63.6
7.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.
(a)30°
(b)45°
(c)120°
(d)60°
8.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.
(a)49°
(b)41°
(c)82°
(d)98°
9.Two straight lines cross at a point. Which statement about a pair of vertically opposite angles is always true?
(a)They are always equal to 90° each
(b)They always add up to 360°
(c)They always add up to 180°
(d)They are always equal to each other
10.An angle measures 108°. Write down the name given to an angle of this size.
(a)An acute angle
(b)A right angle
(c)A reflex angle
(d)An obtuse angle
11.A regular polygon has 12 sides. Work out the size of one exterior angle of the polygon.
(a)30°
(b)150°
(c)15°
(d)36°
12.Two of the angles in a triangle are 50° and 70°. Work out the size of the third angle.
(a)60°
(b)240°
(c)110°
(d)120°
13.Two angles are supplementary. One of them is twice the size of the other. Work out the size of the smaller angle.
(a)30
(b)120
(c)90
(d)60
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.
(a)242
(b)62
(c)118
(d)28
15.The sum of the interior angles of a polygon is 1980°. Work out the number of sides of the polygon.
(a)11
(b)13
(c)22
(d)15

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