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.

VersionsA only A + B A + B + Csame questions, different order

AnswersQuestions only With answer key Key only

CalculatorMixed Non-calculator (Paper 1)Calculator (Papers 2 and 3)

New sheet

Angle facts, parallel lines and polygons worksheet — GCSE Foundation

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

MathsUKwww.geekhero.co.uk

1.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°
2.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
3.Freya is designing a triangular flower bed. Two of its corners have equal angles, and the angle at the third corner is 40°. Work out the size of one of the two equal corner angles.
(a)70°
(b)140°
(c)50°
(d)20°
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 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
6.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°
7.Four angles meet at a point. Three of them measure 82°, 105° and 96°. Work out the size of the fourth angle.
(a)159
(b)283
(c)182
(d)77
8.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.
(a)65
(b)25
(c)115
(d)245
9.At a point on a straight line, two angles are formed. One of them is 63°. Work out the size of the other angle.
(a)297
(b)117
(c)27
(d)63
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.
(a)49°
(b)41°
(c)82°
(d)98°
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.
(a)−10
(b)47.5
(c)25
(d)20
12.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
13.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
14.A regular nonagon has 9 sides. Work out the sum of its interior angles.
(a)1260°
(b)1620°
(c)1440°
(d)140°
15.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

Build your own mix at the worksheet builder.