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

Explanation:

The opposite angles of any quadrilateral that is inscribed in a circle are supplementary. This means that the opposite angles add up to give 180°.

m∠A is supplementary to m∠C. Therefore,

4x + 5 + x + 15 = 180

Collecting like terms, it becomes

4x + x + 15 + 5 = 180

5x + 20 = 180

Subtracting 20 from the Left hand side and the right hand side of the equation, it becomes

5x + 20 - 20 = 180 - 20

5x = 160

Dividing the Left hand side and the right hand side of the equation by 5, it becomes

5x/5 = 160/5

x = 32

Therefore,

m∠A = (4 × 32) + 5

m∠A = 133°