3. Inscribed Angles
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The Inscribed Quadrilateral Theorem says that opposite angles of a quadrilateral inscribed in a circle are supplementary.
a = 112, b = 120, and c = 38
Consider the given diagram.
Let's find the values of a, b, and c one at a time.
Using this theorem, we can find the value of a. a+68=180 ⇔ a=112
By the Arc Addition Postulate, we know that the measure of the intercepted arc of the inscribed angle whose measure is 112^(∘) is the sum of 104^(∘) and b^(∘).
Once again, by the Arc Addition Postulate we know that the measure of the intercepted arc of the inscribed angle whose measure is 71^(∘) is the sum of 104^(∘) and c^(∘).