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

(6x+19)° + x° = 180°
7x° = 180°-19°
7x° = 161°
x = 23°

m∠B = 6(23) + 19
= 157°

Answer 2

∠B=157°

Explanation:

It is given that Quadrilateral ABCD ​is inscribed in the circle.

Also, we know that if the Quadrilateral ABCD ​ is inscribed in the circle, then the opposite angles of the quadrilateral are supplementary by the property of circles. Then,

∠B+∠D=180°

⇒
`x+6x+19=180`

⇒
`7x+19=180`

⇒
`7x=161`

⇒
`x=23^{{\circ}}`

Thus, the value of ∠B=6x+19=6(23)+19=138+19=157°.