Question

Quadrilateral ABCD ​ is inscribed in this circle.

Answer 1

Answer:

∠B=157°

Step-by-step 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°.

Answer 2

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

m∠B = 6(23) + 19
= 157°