Question

Quadrilateral ABCD ​ is inscribed in a circle.

What is the measure of angle A?



Enter your answer in the box.

m∠A=
°

A quadrilateral inscribed in a circle. The vertices of quadrilateral lie on the edge of the circle and are labeled as A, B, C, D. The interior angle A is labeled as left parenthesis 4 x plus 5 right parenthesis degrees. The angle C is labeled as left parenthesis x plus 15 right parenthesis degrees.

Answer 1

The measure of angle A is $\angle A =133^{\circ$

Explanation:

It is given that quadrilateral ABCD is inscribed in a circle.

The measures of $\angle A$ and $\angle C$ is given by

$\angle A = (4x+5)^{\circ}$ and $\angle C=(x+15)^{\circ}$

We need to determine the measure of angle A

Since, in a cyclic quadrilateral, the sum of the opposite angles add upto 180°

Thus, from the given the opposite angles are A and C.

Thus, we have,

$\angle A+\angle C=180^{\circ}$

Substituting the values, we have,

$4x+5+x+15=180$

            $5x+20=180$

                    $5x=160$

                      $x=32$

Thus, substituting $x=32$ in the measure of $\angle A$, we get,

$\angle A = (4x+5)^{\circ}$

$\angle A = (4(32)+5)^{\circ}$

$\angle A = (128+5)^{\circ}$

$\angle A = 133^{\circ}$

Thus, the measure of angle A is $\angle A = 133^{\circ}$

Learn more:

(1) Quadrilateral ABCD ​ is inscribed in this circle. What is the measure of angle C? Enter your answer in the box. ° A quadrilateral inscribed in a circle. The vertices of quadrilateral lie on the edge of the circle and are labeled as A, B, C, and D. The interior angle A is labeled as left parenthesis x plus 15 right parenthesis degrees. The angle B is labeled as left parenthesis x plus 10 right parenthesis degrees. The angle D is labeled as left parenthesis x plus 24 right parenthesis degrees.

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(2) Quadrilateral ABCD ​ is inscribed in this circle. What is the measure of angle B? Enter your answer in the box. m∠B= ° A quadrilateral inscribed in a circle. The vertices of quadrilateral lie on the edge of the circle and are labeled as A, B, C, D. The interior angle B is labeled as left parenthesis 6 x plus 19 right parenthesis degrees. The angle D is labeled as x degrees.

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