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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.

Step-by-step explanation:

Quadrilateral OPQR is inscribed inside a circle as shown in the given diagram. It is a shape bounded by four different sides and four different angles.

In a quadrilateral, the sum of all the angles is equal yo 360 degrees.

This means that

angle O + angle P + angle Q + angle R = 360 degrees.

Also, the opposite angles of the quadrilateral are supplementary. This means that the sum of the opposite angles is 180 degrees. Therefore,

Angle O + angle Q = 180

3y + 8 + y = 180

4y = 180-8 = 172 - - - - - - - -1

Angle R + angle P = 180

2x + 2x + 4 = 180

4x + 4 = 180- - - - - - - -2

From equation 1

y = 172/4 = 43

angle R = 3y + 8

= 3×43 +8 =137 degrees