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

132°

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 = (192)/(4) \\ \\ \implies \: x = 48\\\\`

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

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