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

∠B=132°

Explanation:

It is given that ​ Quadrilateral ABCD ​ is inscribed in this circle and we know that the sum of the opposite angles of the quadrilateral inscribed in the circle equals 180°.

Therefore, ∠D+∠B=180°

⇒
`x+(3x-12)=180`

⇒
`4x=180+12`

⇒
`4x=192^(\circ)`

⇒
`x=48^(\circ)`

Thus, the measure of ∠B is=
`3x-12=3(48)-12=144-12=132^(\circ)`

Answer 2

Assuming the sum of the opposite angle would be 180. We can easily calculate for x and ultimately solve for the angle of B. We do as follows

B + D = 180
3x-12 + x = 180
4x - 12 = 180
4x = 192
x = 48 degrees

Therefore angle B would have a measurement of 132 degrees. Hope this helps.