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vovikov84 [41]
3 years ago
7

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

Mathematics
2 answers:
Contact [7]3 years ago
6 0

Answer:

77°

Step-by-step 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 =  \frac{170}{5}  \\ x = 34 \\ \angle A  = (2 \times 34 + 9) \degree  \\  \huge \red{ \boxed{\angle A= 77 \degree}} \\

Katen [24]3 years ago
4 0

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!

:)

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