The measure of angle B is 132°
Explanation:
Given that the quadrilateral is inscribed in a circle.
The vertices A, B, C, D of a quadrilateral lie on the edge of the circle.
The angle B is given by [tex]\angle B=(3x-12)^{\circ}[/tex]
The angle D is given by [tex]\angle C=x^{\circ}[/tex]
We need to find the measure of angle B.
Since, the angles B and D are opposite angles.
Also, we know that the opposite angles of a quadrilateral are supplementary.
Thus, we have,
[tex]\angle B+\angle D=180^{\circ[/tex]
Substituting the values, we get,
[tex]3x-12+x=180[/tex]
[tex]4x-12=180[/tex]
[tex]4x=192[/tex]
[tex]x=48[/tex]
Thus, the value of x is 48
Substituting the value of x in the angle B, we get,
[tex]\angle B=(3(48)-12)^{\circ}[/tex]
[tex]\angle B=(144-12)^{\circ}[/tex]
[tex]\angle B=132^{\circ}[/tex]
Thus, the measure of angle B is [tex]\angle B=132^{\circ}[/tex]
Answer: 132
Step-by-step explanation: Just confirming the answer :)
