The angle at the center is twice the angle at the circumference when both stand on the same arc. So if ∠ACB = 33°, then ∠AOB = 66°.
Angles in the same segment are equal: angles at the circumference standing on the same chord are the same size. The angle in a semicircle is 90°. Opposite angles in a cyclic quadrilateral, one with all four corners on the circle, add up to 180°.
Worked example
ABCD is a cyclic quadrilateral. ∠ABC = 66°. Find ∠ADC.
- Opposite angles of a cyclic quadrilateral add to 180°.
- 180 − 66 = 114.
Answer:114°
Key words
- circumference
- the edge of the circle
- cyclic quadrilateral
- all four vertices on the circle
- segment
- the region between a chord and an arc
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Common Core-referenced: HSG-C.A.2