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Mathematics · Topic

Angles, polygons and parallel lines

Give the angle reason by name — the reason is an actual mark.

2 original questions in the bank, worth 4 marks · above the two-per-topic floor

Drill this topic All angles, polygons and parallel lines questions

The questions, with the examiner reasoning

Find1 markIGCSE

Each exterior angle of a regular polygon is 24°. How many sides does the polygon have?

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Answer: 15

  1. Exterior angles of a polygon sum to 360°
  2. 360 ÷ 24 = 15 sides
  • A. 15 — Correct: exterior angles of any polygon total 360°, and 360 ÷ 24 = 15.
  • B. 12 — That would give exterior angles of 30°.
  • C. 24 — The exterior angle was copied as the number of sides.
  • D. 16 — A rounding slip: 24 × 15 = 360 exactly, so no rounding is needed.

Examiner technique: The exterior angle fact does all the work in polygon questions. Interior angles total 180(n − 2), which is slower and easier to get wrong.

Find3 marksBGCSE

In triangle ABC, angle A = 2x, angle B = 3x and angle C = 4x. Find the value of x and the size of the largest angle.

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Answer: x = 20°, largest angle = 80°

  1. Angles in a triangle total 180°: 2x + 3x + 4x = 180
  2. 9x = 180, so x = 20
  3. Largest angle = 4 × 20 = 80°

Examiner technique: Two marks are given here even if the arithmetic slips, provided the equation is right. Write the equation, then solve it.