Question

Quadrilateral ABCD is inscribed in circle O. What is ​ m∠B ​ ? Enter your answer in the box. ° A quadrilateral is inscribed in a circle O. The vertices of the quadrilateral lie on the edge of the circle and are labeled as A, B, C, and D. The interior angle A is labeled as left parenthesis 2 x minus 7 right parenthesis. The angle B is labeled as left parenthesis 2 x plus 3 right parenthesis. The angle C is labeled as left parenthesis x plus 4 right parenthesis.

Answer 1

Question: Quadrilateral ABCD is inscribed in circle O. What is ​ m∠B ​ ? Enter your answer in the box. ° A quadrilateral is inscribed in a circle O. The vertices of the quadrilateral lie on the edge of the circle and are labeled as A, B, C, and D. The interior angle A is labeled as left parenthesis 2 x minus 7 right parenthesis. The angle B is labeled as left parenthesis 2 x plus 3 right parenthesis. The angle C is labeled as left parenthesis x plus 4 right parenthesis.

Answer:

Answer 2

`m<B=125\°`

Explanation:

Step 1

Find the value of x

we know that

In an inscribed quadrilateral the opposites angles are supplementary

so

In this problem

`m<A+m<C=180\°`

substitute the values and solve for x

`(2x-7)+(x+4)=180\°`

`3x-3=180\°`

`3x=183\°`

`x=183\°/3=61\°`

step 2

Find the measure of angle B

`m<B=(2x+3)`

substitute the value of x

`m<B=(2(61)+3)\°=125\°`