Question

Quadrilateral ABCD ​ is inscribed in this circle.

Answer 1

The measure of angle A is 65°

Explanation:

Given that ABCD is a quadrilateral inscribed in a circle.

The measure of angle A is $\angle A=(2x+1)^{\circ}$

The measure of angle B is $\angle B=148^{\circ}$

The measure of angle D is $\angle D=x^{\circ}$

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,

$\angle B+\angle D=180^{\circ}$

Substituting the values, we have,

$148^{\circ}+x=180^{\circ}$

          $x=32^{\circ}$

Thus, the value of x is 32°

Substituting the value of x in the measure of angle A, we get,

$\angle A=(2x+1)^{\circ}$

$\angle A=(2(32)+1)^{\circ}$

$\angle A=(64+1)^{\circ}$

$\angle A=65^{\circ}$

Thus, the measure of angle A is 65°