Question

Quadrilateral ABCD​ is inscribed in this circle.



What is the measure of angle B?

Enter your answer in the box.

m∠B=
°

Answer 1

Answer:

132°

Step-by-step explanation:

Quadrilateral ABCD is inscribed in a circle,

So, it is a cyclic quadrilateral.

Opposite angles of a cyclic quadrilateral are supplementary.

$\implies \: x \degree + (3x - 12) \degree = 180 \degree \\ \\ \implies \: (4x - 12) \degree = 180 \degree \\ \\ \implies \: 4x - 12 = 180 \\ \\ \implies \: 4x = 180 + 12 \\ \\ \implies \: 4x = 192 \\ \\ \implies \: x = \frac{192}{4} \\ \\ \implies \: x = 48$

(3x-12)° = (3*48 - 12)° = (144 - 12)° = 132°

$\implies \: m\angle B = 132\degree$