please help me fix my mistake! will medal + fan

Quadrilateral OPQR is inscribed in circle N, as shown below. What is the measure of ∠ROP?

My answer: 67

Question

please help me fix my mistake! will medal + fan

Quadrilateral OPQR is inscribed in circle N, as shown below. What is the measure of ∠ROP?

My answer: 67

math_genius12345 · Answer

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mww · Answer

It might help you to know opposite angles of a cyclic quad are supplementary,

mww · Answer

Thus Angles O and Q add to 180

math_genius12345 · Answer

@mww thank you! could you help me find the measure of the other one as well?

princeharryyy · Answer

Sum of opposite angles is 180 deg so, x + 17 + 6x-5 = 180,
7x+12=180,
X= 168/7 = 24,
Angle rop = x+17=24+17=41

princeharryyy · Answer

Sum of opposite angles is 180 deg so, x + 17 + 6x-5 = 180,
7x+12=180,
X= 168/7 = 24,
Angle rop = x+17=24+17=41

math_genius12345 · Answer

@princeharryyy I think you're right! thanks so much!