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The measure of angle A is 65°
Explanation:
Given that ABCD is a quadrilateral inscribed in a circle.
The measure of angle A is
The measure of angle B is
The measure of angle D is
We need to determine the measure of angle A.
Since, we know that the angles B and D are opposite angles and the opposite angles of a quadrilateral add up to 180°
Thus, we have,
Substituting the values, we have,
Thus, the value of x is 32°
Substituting the value of x in the measure of angle A, we get,
Thus, the measure of angle A is 65°