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Geometry and measuresFoundation and Higher

Angles and bearings GCSE questions with answers

8 angles and bearings questions to try, each with the answer and the full working one tap away. Every question here was made and worked out by the Show Working maths engine, not typed in by hand.

Angle questions use the facts for triangles, quadrilaterals, straight lines, angles round a point and parallel lines, plus angles in polygons and three-figure bearings. Many take two or more steps, and some build an equation from the angles.

Quiz yourself: 8 questions

Worked example 1: angles in a triangle

Work out the size of angle x.

x68°
Not drawn accurately
  1. The two sides with dashes are equal, so the triangle is isosceles and its two base angles are equal.
  2. The base angles together: 180° − 68° = 112°.
  3. Each base angle: 112° ÷ 2 = 56°, so x = 56°.

Answer 56°

01 / Quiz yourselfTry it, then tap to check

Angles and bearings questions to try

Work each one out on paper first. Then open the answer and compare your working with ours, step by step.

01 / Angles in a triangleBoth tiers

Work out the size of angle x.

x70°
Not drawn accurately
Show the answer and working
  1. The two sides with dashes are equal, so the triangle is isosceles and its two base angles are equal.
  2. The base angles together: 180° − 70° = 110°.
  3. Each base angle: 110° ÷ 2 = 55°, so x = 55°.

Answer 55°

02 / Angles on a line and round a pointBoth tiers

The angles meet at a point. Work out the size of angle x.

x76°129°
Not drawn accurately
Show the answer and working
  1. Angles round a point add up to 360°.
  2. The angles you know add up to 129° + 76° = 205°.
  3. x = 360° − 205° = 155°.

Answer 155°

03 / Angles and parallel linesBoth tiers

The two lines with arrows are parallel. Work out the size of angle x.

122°x
Not drawn accurately
Show the answer and working
  1. The two angles are between the parallel lines, on opposite sides of the crossing line (a Z shape helps you spot them). Alternate angles are equal.
  2. x = 122°.
  3. In an exam, write the reason in full, like "Alternate angles are equal". "Z angles" or "C angles" do not get the mark.

Answer 122°

04 / Angles in quadrilateralsBoth tiers

Work out the size of the angle marked x.

134°79°86°x
Not drawn accurately
Show the answer and working
  1. The angles inside a quadrilateral add up to 360°.
  2. The three angles you know add up to 134° + 79° + 86° = 299°.
  3. x = 360° − 299° = 61°.

Answer 61°

05 / Angles in polygonsBoth tiers

Work out the sum of the interior angles of a hexagon.

Not drawn accurately
Show the answer and working
  1. A hexagon has 6 sides. From one corner you can split it into 6 − 2 = 4 triangles.
  2. Each triangle has 180°, so the angles add up to 4 × 180° = 720°.

Answer 720°

06 / BearingsBoth tiers

The bearing of B from A is 054°. Work out the bearing of A from B.

NNAB054°
Not drawn accurately
Show the answer and working
  1. A bearing is measured clockwise from north. The way back points in exactly the opposite direction, so it differs by 180°.
  2. 054° + 180° = 234°.

Answer 234°

07 / Angle problems with two or more stepsBoth tiers

BCD is a straight line. Work out the size of the angle marked x.

ABCD70°142°x
Not drawn accurately
Show the answer and working
  1. Angles on a straight line add up to 180°: angle ACB = 180° − 142° = 38°.
  2. Angles in a triangle add up to 180°: x = 180° − 70° − 38° = 72°.
  3. (Or: the exterior angle equals the sum of the two interior opposite angles, so x = 142° − 70°.)

Answer 72°

08 / Angles in quadrilaterals with algebraBoth tiers

The diagram shows a quadrilateral. Work out the size of its largest angle.

2x−153x+53x−10x+20
Not drawn accurately
Show the answer and working
  1. The angles in a quadrilateral add up to 360°, so add the four angles and make them equal 360.
  2. (2x − 15) + (3x + 5) + (3x − 10) + (x + 20) = 360
  3. Collect the x terms and the numbers: 9x = 360
  4. 9x = 360, so x = 360 ÷ 9 = 40.
  5. The largest angle is 3x + 5 = 3 × 40 + 5 = 125°.

Answer 125°

02 / What's covered8 kinds of question

Angles and bearings at GCSE and where marks go

  • Angles in a triangleBoth tiers
  • Angles on a line and round a pointBoth tiers
  • Angles and parallel linesBoth tiers
  • Angles in quadrilateralsBoth tiers
  • Angles in polygonsBoth tiers
  • BearingsBoth tiers
  • Angle problems with two or more stepsBoth tiers
  • Angles in quadrilaterals with algebraBoth tiers

Worked example 2: angles in quadrilaterals with algebra

The diagram shows a quadrilateral. The angles are in degrees. Work out the value of x.

2x+303x−202x+203x
Not drawn accurately
  1. The angles in a quadrilateral add up to 360°, so add the four angles and make them equal 360.
  2. (2x + 30) + (3x − 20) + (2x + 20) + (3x) = 360
  3. Collect the x terms and the numbers: 10x + 30 = 360
  4. 10x = 330, so x = 330 ÷ 10 = 33.

Answer x = 33

A common mistake

Mixing up interior and exterior angles. The exterior angles of any polygon add up to 360°, so each exterior angle of a regular hexagon is 360° ÷ 6 = 60°, and each interior angle is 180° − 60° = 120°.

03 / Practise itiPhone and iPad

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