Quadrilateral opqr is inscribed in circle n, as shown below. which of the following could be used to calculate the measure of ∠opq? answers: a) m∠opq + (2x + 16)° = 180° b)m∠opq = (6x − 4)° + (2x + 16)° c)m∠opq + (x + 16)° + (6x − 4)°= 360° d)m∠opq = (x + 16)° + (6x − 4)°

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

after simplifying it i got: -36.25 as my answer. hope that !