Maths worksheets · lesson 53 of 64 · free

Triangles: angle sum, exterior angle and Pythagoras — Maths worksheet

The three angles of any triangle add up to 180°. If one side is extended, the exterior angle equals the sum of the two interior angles opposite it. In an isosceles triangle two angles are equal. In a right-angled triangle, Pythagoras says longest side² = sum of the squares of the other two sides. And three lengths make a triangle only if the two shorter ones add up to more than the longest.

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The method

Inside 180, outside the sum — “the angles add up to 180°; an exterior angle equals the two opposite interior angles”

  1. Angle sum: ∠A + ∠B + ∠C = 180°.
  2. Exterior angle = sum of the two interior opposite angles.
  3. Right-angled triangle: longest side² = side² + side² (3, 4, 5 and 5, 12, 13 are famous sets).
  4. Sides can make a triangle only if the two shorter sides add up to more than the longest side.

Use it for: Roof frames, ladders against walls, shortcuts across a field, and the triangles chapter of Class 7 maths.

Worked example: An exterior angle of a triangle is 110°. One of its two interior opposite angles is 45°. What is the other one (in degrees)? → 65

  1. An exterior angle equals the sum of the two interior opposite angles.
  2. 110 − 45 = 65.

Check: 45 + 65 = 110 ✓, and the third angle 180 − 110 = 70 makes 45 + 65 + 70 = 180 ✓

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🏁 Lesson 53 test

20 sums. Check each answer, then go to the next one. Get 16 or more right to pass.

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🖨️ Class 7 Maths Worksheet: Triangles

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