Question: quadrilateral opqr is inscribed inside a circle as shown below. what is the measure of angle r? you must show all work and calculations to receive credit.

m<R = 137°

Step-by-step explanation:

Points to remember

Sum of opposite angles of a cyclic quadrilateral is 180°.

From the figure we can see a cyclic quadrilateral.

To find the value of y

From the figure we get angle R and angle P are opposite to each other.

m<R = 3y + 8 and  m<P = y

m<R + m<P = 180

3y + 8 + y = 180

4y + 8 = 180

4y = 180 - 8 = 172

y = 172/4 = 43

To find the measure of R

m<R = 3y + 8

 = 3*43 + 8

 = 129  + 8 = 137

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