Question

Quadrilateral ABCD is inscribed in this circle.

What is the measure of angle A?
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Answer 1

m∠A = 116°

Explanation:

For better understanding of the solution, see the attached figure of the problem :

The quadrilateral ABCD is inscribed in a circle, Thus the quadrilateral ABCD is a cyclic quadrilateral.

Also, Sum of opposite angles of a cyclic quadrilateral is supplementary.

Now, m∠A = (x - 36)°, m∠B = 28° and m∠D = x°

But, since the sum of opposite angles is 180°

⇒ 28° + x° = 180°

⇒ x = 180 - 28

⇒ x = 152

So, m∠A = (x - 36)°

⇒ m∠A = (152 - 36)°

⇒ m∠A = 116°