Maths Olympiad · topic 21 of 33 · free

Angles and triangles — Maths Olympiad practice

Most angle questions need just a few facts: the angles of a triangle add up to 180°, so do angles on a straight line, and vertically opposite angles are equal. Olympiad options are built from the usual slips — using 360° instead of 180°, or forgetting that an isosceles triangle has two equal angles.

How to solve it

180 is the magic number — “a triangle and a straight line both add up to 180°”

  1. The three angles of a triangle add up to 180°.
  2. An exterior angle equals the sum of the two interior angles opposite it.
  3. An isosceles triangle has two equal angles, opposite its two equal sides.
  4. Angles on a straight line add up to 180°; vertically opposite angles are equal.

Use it for: Triangle, straight-line and crossing-lines questions in Class 6–10 Olympiad papers and geometry chapters.

Worked example: In an isosceles triangle, the angle between the two equal sides is 50°. What is each of the other two angles? 65°

  1. The other two angles are equal and together make 180° − 50° = 130°.
  2. Share it equally: 130 ÷ 2 = 65, so each angle is 65°.

Check: 65° + 65° + 50° = 180° ✓

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🖨️ Angles and Triangles Worksheet for Maths Olympiad

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