Question

​ Quadrilateral ABCD ​ is inscribed in this circle. What is the measure of angle B? Enter your answer in the box. m∠B= ° A quadrilateral inscribed in a circle. The vertices of the quadrilateral lie on the edge of the circle and are labeled as A, B, C, D. The interior angle B is labeled as left parenthesis 3 x minus 12 right parenthesis degrees. The angle D is labeled as x degrees.

Answer 1

Answer:

Quadrilateral ABCD is inscribed in this circle. What is the measure of angle B? Enter your answer in the box. m∠B= ° A quadrilateral inscribed in a circle. The vertices of the quadrilateral lie on the edge of the circle and are labeled as A, B, C, D. The interior angle B is labeled as left parenthesis 3 x minus 12 right parenthesis degrees. The angle D is labeled as x degrees.

Answer 2

The measure of angle B is 132°

Step-by-step explanation:

given : Quadrilateral ABCD ​ is inscribed in this circle

$\angle B = (3x-12) \\\\\angle D = x$

we need to find the angle B

solution :

since we know that the sum of the opposite angles of a cyclic quadrilateral is 180 degrees

therefore

in quadrilateral ABCD

$\angle B + \angle D = 180^\circ\\\\3x-12 +x=180\\\\4x= 180+12\\\\4x=192\\\\x=\frac{192}{4}\\\\ x= 48^\circ$

then place the value of x in angle B

$\angle B = 3x-12\\\\x= 48^\circ \\\\\angle B = 3(48) -12\\\\\angle B = 144-12\\\\\angle B = 132^\circ$

hence , The measure of angle B is 132°

#Learn more:

Quadrilateral ABCD ​ is inscribed in a circle.

What is the measure of angle A?

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