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Maths

Circles - Higher

Opposite angles in a cyclic quadrilateral add up to 180°

A cyclic quadrilateral is a quadrilateral whose vertices all touch the circumference of a circle. The opposite angles add up to 180o.

In the cyclic quadrilateral below, angles A + C = 180o, and angles B + D = 180o.

image: circle with a quadrilateral shape inside: top corner: A, right: B, bottom: C, left: D.

Question

What is the size of:

  1. angle A?
  2. angle B?
image: circle with a quadrilateral shape inside: top corner: B, upper right: A, lower right: 140 degrees, bottom: 60 degrees.

toggle answer

Answer
  1. A + 60° = 180°, so A = 120°.
  2. B + 140° = 180°, so B = 40°.

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