Answer:
The measure of the ∠A is 59°.
Explanation:
It is given that a quadrilateral ABCD is inscribed in a circle, and from the properties of circle, we know that the sum of the opposite angles of the quadrilateral inscribed in the circle is equal to 180°.
Therefore, ∠A+∠C=180°
⇒

⇒

⇒

Therefore, the measure of the ∠A is 59°.