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3.4 Angle facts

Angle facts

Everything on angle facts that can come up in the WJEC GCSE Mathematics and Numeracy, in Unit 2 and Unit 3. Each skill below has the method, the mistake that costs the most marks, a worked example, and free practice marked the way WJEC marks it.

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A worked example

Polygons · [2 marks]

Work out the sum of the interior angles of a 11-sided polygon.

  1. M1(11 − 2) × 180
  2. A11620°

The exam skills (8)

Angles on a line

  1. Angles on a straight line add up to 180°.
  2. Take the known angles away from 180.
  3. Write the reason in full.

Watch out: Losing the reason mark. Write "angles on a straight line add up to 180°".

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Angles round a point

  1. Angles around a point add up to 360°.
  2. Take the known angles away from 360.
  3. Write the reason in full.

Watch out: Using 180°. All the way round is 360°.

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Angles in a triangle

  1. Angles in a triangle add up to 180°.
  2. Take the two known angles away from 180.
  3. Write the reason.

Watch out: Writing "it is a triangle" as a reason. Say what adds up to what.

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Isosceles triangles

  1. An isosceles triangle has two equal angles, at the base of the equal sides.
  2. If you know the top angle: (180 − top) ÷ 2.
  3. If you know a base angle: the other base angle is the same.

Watch out: Making the wrong two angles equal. The equal angles are opposite the equal sides.

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Parallel lines

  1. Alternate angles (Z shape) are equal.
  2. Corresponding angles (F shape) are equal.
  3. Co-interior angles (C shape) add up to 180°.

Watch out: Using the shape name without the word: write "alternate angles", not "Z angles".

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Polygons

  1. Sum of interior angles = (number of sides − 2) × 180°.
  2. Exterior angles of any polygon add up to 360°.
  3. Regular polygon: each exterior angle = 360 ÷ sides.

Watch out: Using n × 180. Take 2 off first.

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Angles and algebra

  1. Write an equation: the angles add up to 180 or 360.
  2. Collect the x terms and the numbers, then solve.
  3. Substitute x back in to find the angle the question asks for.

Watch out: Stopping at x. The question usually wants an angle.

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Circle theorems

  1. The angle at the centre is twice the angle at the circumference.
  2. Both angles must come from the same two points (the same arc).
  3. Halve or double, then write the theorem as your reason.

Watch out: Halving when you should double.

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