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andrey2020 [161]
3 years ago
11

​ Quadrilateral ABCD ​ is inscribed in this circle.

Mathematics
2 answers:
Kaylis [27]3 years ago
4 0

Answer:

∠B=132°

Step-by-step 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}

fgiga [73]3 years ago
3 0
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.
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