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.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
2.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.
(a)90°
(b)55°
(c)35°
(d)125°
3.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
4.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.
(a)19
(b)10
(c)20
(d)14
5.Angle ABC is 130°. The line BF divides angle ABC into two equal parts. Work out the size of angle FBC.
(a)65°
(b)32.5°
(c)50°
(d)130°
6.Which of these describes an obtuse angle?
(a)An angle between 180° and 360°
(b)An angle between 90° and 180°
(c)An angle of exactly 90°
(d)An angle between 0° and 90°
7.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
8.Three angles lie on a straight line. They measure 38°, 95° and x°. Work out the value of x.
(a)133
(b)47
(c)227
(d)142
9.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
10.A regular nonagon has 9 sides. Work out the sum of its interior angles.
(a)1260°
(b)1620°
(c)1440°
(d)140°
11.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
12.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
13.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.
(a)225
(b)45
(c)315
(d)135
14.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
15.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°

Build your own mix at the worksheet builder.