Anyone teach me the angles in theorms

The alternate segment theorem says that angles BAC and BCE are congruent, so

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Triangle ABC is isosceles, which makes angles ACB and ABC congruent, and the sum of the interior angles of any triangle is 180 degrees, so

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The alternate segment theorem also says that angles DCF and CAD are congruent. Angles DCF, ACD, ACB, and BCE are supplementary, so

Then

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The inscribed angle theorem says that angle COB has twice the measure of angle BAC, so

the answer is 62.8 cubic units