geometry · Year 7 · Suggested learning sequence

Angles in a quadrilateral

Any quadrilateral can be cut corner to corner into two triangles, so its four angles add up to 2 × 180 = 360°. Add the angles you know and take the total away from 360. Count a small square as 90°. When two angles have the same letter they are equal, so share what is left between them. The diagram is not drawn to scale.

Sample questions

Find the missing angle in the quadrilateral, marked with a question mark. The diagram is not drawn to scale.

70°65°115°?Not drawn to scale
  1. The angles in a quadrilateral add up to 360°.
  2. Add the angles you know: 70 + 65 + 115 = 250.
  3. 360 − 250 = 110, so the missing angle is 110°.

Answer: 110

Find the missing angle in the quadrilateral, marked with a question mark. The diagram is not drawn to scale.

65°115°?60°Not drawn to scale
  1. The angles in a quadrilateral add up to 360°.
  2. Add the angles you know: 65 + 115 + 60 = 240.
  3. 360 − 240 = 120, so the missing angle is 120°.

Answer: 120

Find the missing angle in the quadrilateral, marked with a question mark. The diagram is not drawn to scale.

100°60°?120°Not drawn to scale
  1. The angles in a quadrilateral add up to 360°.
  2. Add the angles you know: 100 + 60 + 120 = 280.
  3. 360 − 280 = 80, so the missing angle is 80°.

Answer: 80

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