Let O be the centre of a circle. Let A, B and C lie on the circle such that ∠ABC = 153°. What is the value of ∠AOC?
A.54°✓ Correct
B.52°
C.39°
D.27°
Explanation
When ∠ABC = 153° > 90°, B is on the minor arc, and the angle at the center subtending the major arc AC (not containing B) equals 2 × ∠ABC = 306°. So the reflex ∠AOC = 306°, meaning the (non-reflex) ∠AOC = 360° − 306° = 54°.
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