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MathidiaMathematics Academy
Angles and constructions
Lesson 59 of 75
Challenge

Angles in triangles and quadrilaterals

Objective. Use interior angle sums to find unknown angles.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

The interior angles of any triangle always sum to 180°, while the interior angles of any quadrilateral always sum to 360°. These facts let you find a missing angle when the others are known, by subtracting the known angles from the total. For example, in a triangle with angles 50° and 65°, the third angle is 180−50−65=65°. In a quadrilateral with angles 90°, 85° and 100°, the fourth angle is 360−90−85−100=85°.

Worked example

A triangle has angles of 48° and 72°. Find the size of the third angle in the triangle.

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Fraction bar showing 1 out of 3 parts shaded
  1. 1Recall that angles in a triangle sum to 180°.
  2. 2Add the two known angles: 48+72=120.
  3. 3Subtract from 180: 180−120=60.
  4. 4State the size of the third angle.

Answer: 60°

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Common mistake. Pupils sometimes use 180° as the angle sum for a quadrilateral, confusing it with a triangle's angle sum. Always check the number of sides of the shape before choosing 180° or 360°.

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