Question

​ Quadrilateral ABCD ​ is inscribed in this circle. What is the measure of ∠A ? Enter your answer in the box. ° A quadrilateral inscribed in a circle. The vertices of the quadrilateral lie on the edge of the circle and are labeled A, B, C, D. The interior angle C is labeled as 74 degrees.

Answer 1

Answer:

angle A = 106 degrees

Step-by-step explanation:

As all the vertices of quad ABCD touch the circle, the quadrilateral is a cyclic quadrilateral.

We know that the opposite angles of a cyclic quadrilateral are supplementary

Therefore, angle A + angle C = 180 degrees

Given, angle C = 74 degrees

This implies that    angle A + 74 degrees = 180 degrees

Which gives us   angle A = 106 degrees

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Answer 2

Answer:

106 degrees

Step-by-step explanation:

In a cyclic quadrilateral opposite angles are supplementary .

So , angle A +angle C = 180 Degrees

         angle A + 74 = 180

                 angle A = 180 - 74

                 angle A = 106 degrees