Quadrilateral ABCD is inscribed in this circle. What is the measure of ∠A ?

Question

I got 106, is my answer correct?

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Answer 1 · 2017-05-12T13:44:48

Yes

A cyclic quadrilateral is a quadrilateral that is inscribed in a circle, which has the property that opposite angles are supplementary.

Therefore:
$∠ A + ∠ C = 180^{\circ}$ $angleA+angleC=180^@$
$∠ A + 74^{\circ} = 180^{\circ}$ $angleA+74^@=180^@$
$∠ A = 106^{\circ}$ $angleA=106^@$

So, your answer is correct.

Hope this helps.