Question

Quadrilateral ABCD is inscribed in this circle. What is the measure of angle B?

Answer 1

Angle B measures to 132 degrees.

Answer 2

∠B = 132°

Explanation:

Quadrilateral ABCD is inscribed in the given circle.

And if a quadrilateral is inscribed inside a circle then the quadrilateral is called cyclic quadrilateral.

And the sum of opposite angles of a cyclic quadrilateral is supplementary that is 180

⇒ Sum of opposite angles of the quadrilateral ABCD is 180

⇒ ∠A + ∠C = 180° and ∠B + ∠D = 180°

Now, ∠B + ∠D = 180°

⇒ 3x - 12 + x = 180

⇒ 4x - 12 = 180

⇒ 4x = 180 + 12

⇒ 4x = 192

⇒ x = 48

So, ∠B = 3x - 12

⇒ ∠B = 3 × 48 - 12

⇒ ∠B = 144 - 12

⇒ ∠B = 132°