227k views
1 vote
Quadrilateral ABCD is inscribed in a circle
What is the measure of angle A?

Quadrilateral ABCD is inscribed in a circle What is the measure of angle A?-example-1

2 Answers

4 votes

Answer:

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}} \\

User Diego Sevilla
by
8.3k points
1 vote

Answer:

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!

:)

User Tana
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories