QQuestion
BOC is a diameter of a circle whose centre is O. ABCD is a cyclic quadrilateral. If ∠ADC =110°, find ∠ACB
✓Answer
In cyclic quadrilateral ABCD, opposite angles are supplementary
⇒ ∠ABC + ∠ADC = 180°
⇒ ∠ABC = 180° − ∠ADC = 180° − 110° = 70°.
BC is a diameter (BOC is diameter)
⇒ angle in a semicircle is 90°
⇒ ∠BAC = 90°.
In triangle ABC angles sum to 180°:
∠BAC + ∠ABC + ∠ACB = 180°
⇒ 90° + 70° + ∠ACB = 180°
⇒ ∠ACB = 20°
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