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.

Answer 1

Answer:

137°

Step-by-step explanation:

Opposite angles of inscribed (cyclic) quadrilateral are supplementary.

m∠R + m∠P = m∠O + m∠Q = 180°

Substitute and solve for y:

3y + 8 + y = 180

4y + 8 = 180

4y = 172

y = 172/4

y = 43

Find the measure of angle R:

m∠R = 180 - 43 = 137

Step-by-step explanation:

Answer 2

Answer:

• 137°

Step-by-step explanation:

Opposite angles of inscribed (cyclic) quadrilateral are supplementary.

• m∠R + m∠P = m∠O + m∠Q = 180°

Substitute and solve for y:

• 3y + 8 + y = 180
• 4y + 8 = 180
• 4y = 172
• y = 172/4
• y = 43

Find the measure of angle R:

• m∠R = 180 - 43 = 137