In a circle centered on O AC and BD are diameters. The central angle of the AOD is 128 °. Find the inscribed angle of the ACB.

bystudin | May 31, 2020 | Education

∠AOB – adjacent corner of the AOD. Hence:
∠AOB = 180 ° -∠AOD = 180 ° -128 ° = 52 °
∠AOB is central, and therefore equal to the degree measure of the arc on which it relies.
∠ACB is the inscribed angle, and therefore equal to half the degree measure of the arc on which it rests.
∠ACB = 52 ° / 2 = 26 °
Answer: 26

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