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smc

geometry intermediate

Problem

Triangle is inscribed in a circle. The measure of the non-overlapping minor arcs , and are, respectively, . Then one interior angle of the triangle is:
(A)
(B)
(C)
(D)
Solution
Because the triangle is inscribed, the sum of the minor arcs equals . Thus, Solving this yields , so the inscribed angles are , , and . Noting that an angle of is half of its corresponding inscribed angle, so the angles of are , , and .
Final answer
D