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 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 6 x plus 19 right parenthesis degrees. The angle D is labeled as x degrees.

Answer 1

Answer:

m∠B = 157°

Step-by-step explanation:

Cyclic quadrilateral is the quadrilateral whose vertices lie on the edge of the circle

In the cyclic quadrilateral each two opposite angles are supplementary (the sum of their measures is 180°)

∵ Quadrilateral ABCD is inscribed in a circle

- That means its four vertices lie on the edge of the circle

∴ ABCD is a cyclic quadrilateral

Each two opposite angles in the cyclic quadrilateral are supplementary (The sum of their measures is 180°)

∵ ∠B and ∠D are opposite angles in the quadrilateral ABCD

∴ m∠B + m∠D = 180° ⇒ opposite ∠s in a cyclic quadrilateral

∵ m∠B = (6x + 19)°

∵ m∠D = x°

- Substitute them in the rule above

∴ (6x + 19) + x = 180

- Add the like terms in the left hand side

∴ (6x + x) + 19 = 180

∴ 7x + 19 = 180

- Subtract 19 from both sides

∴ 7x = 161

- Divide both sides by 7

∴ x = 23

Substitute the value of x in the expression of the measure of ∠B to find its measure

∵ m∠B = 6(23) + 19

∴ m∠B = 138 + 19

∴ m∠B = 157°