The opposite angles of the quadrilateral add up to 180°, so x + (3x - 12) = 180.
Since 4x = 192, x = 48.
Hence, angle B equals 3(48) - 12 = 132°.
A quadrilateral is a polygon that has four sides. The measure of the ∠B is 132°.
A quadrilateral is a polygon that has four sides.
In a quadrilateral that is inscribed in a circle, the sum of the opposite angles of the quadrilateral is 180°.
As the ∠D and ∠B are the opposite angles of a quadrilateral, therefore, the sum of the two angles is 180°.
[tex]\angle B+ \angle D = 180^o\\\\(3x-12)+x = 180^o\\\\3x-12+x=180^o\\\\4x=180^o+12^o\\\\4x = 192^o\\\\x = 48^o[/tex]
Now, substituting the value of x in the measure of ∠B, we will get,
[tex]\begin{aligned}\angle B &= 3x-12\\\\&=3(48)-12\\\\&=144-12\\\\&=132^o\end{aligned}[/tex]
Hence, the measure of the ∠B is 132°.
Learn more about Quadrilateral:
https://brainly.com/question/6321910
