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

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

4x-20 + x = 180

5x - 20 = 180

5x = 192

x = 38.4 degrees

Therefore angle B would have a measurement of 141.6 degrees. Hope this helps.

Answer 2

∠ B = 140°

Explanation:

quadrilateral ABCD is a cyclic quadrilateral

the opposite angles of a cyclic quadrilateral sum to 180°

∠ B + ∠ D = 180

4x - 20 + x = 180

5x - 20 = 180 ( add 20 to both sides )

5x = 200 ( divide both sides by 5 )

x = 40

then

∠ B = 4x - 20 = 4(40) - 20 = 160 - 20 = 140°