Question

Which equation could be used to solve for the measure of angle P?

Answer 1

Answer:

Correct choice is B

Step-by-step explanation:

Consider inscribed quadrilateral OPQR in the circle. In thes quadrilateral $m\angle O=x^{\circ},\ m\angle P=y^{\circ},\ m\angleQ=z^{\circ},\ m\angle R=w^{\circ}.$

By the Inscribed Quadrilateral Theorem, a quadrilateral is inscribed in a circle if and only if the opposite angles are supplementary. Thus,

$m\angle O+m\angle Q=180^{\circ},\\ \\m\angle P+m\angle R=180^{\circ}$

or in terms of $x,\ y, z,\ w:$

$x^{\circ}+z^{\circ}=180^{\circ},\\ \\y^{\circ}+w^{\circ}=180^{\circ}.$

Hence, option B is true.

Answer 2

Y+w=180 is the answer.