Question

Quadrilateral ABCD is inscribed in a circle
What is the measure of angle A?

Answer 1

77°

Explanation:

ABCD is inscribed in a circle. Therefore it is a cyclic quadrilateral. Opposite angles of a cyclic quadrilateral are supplementary.

`\therefore \angle A + \angle C = 180° \\ (2x + 9) \degree + (3x + 1) \degree =180° \\ (5x + 10) \degree =180° \\ 5x + 10 = 180 \\ 5x = 180 - 10 \\ 5x = 170 \\ x = (170)/(5) \\ x = 34 \\ \angle A = (2 * 34 + 9) \degree \\ \huge \red{ \boxed{\angle A= 77 \degree}} \\`

Answer 2

Quadrilateral ABCD is inscribed in a circle, then

A + C = 180

=> 2x + 9 + 3x + 1 = 180

=> 5x = 170

=> x = 34

=> A = 2 x 34 + 9 = 77 deg

Hope this helps!

:)