Quadrilateral ABCD is inscribed in this circle.

What is the measure of angle 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 A is labeled as left parenthesis 2 x plus 1 right parenthesis degrees. The angle B is labeled as 148 degrees. The angle D is labeled as x degrees.

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°

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