Quadrilateral OPQR is inscribed in circle N, as shown below. What is the measure of ∠ROP?
2 answers:
Answer: The correct option is (A) 41°.
Step-by-step explanation: Given that quadrilateral OPQR is inscribed in circle N as shown in the figure.
Also, ∠ROP = (x+17)° and ∠RQP = (6x-5)°.
We are to find the measure of ∠ROP.
Since quadrilateral OPQR is inscribed in a circle, so it is a cyclic quadrilateral.
We know that the sum of the measures of opposite angles of a cyclic quadrilateral is 180°.
So, in cyclic quadrilateral OPQR, we have
Therefore, we get
Thus, the measure of angle ROP is 41°.
Option (A) is CORRECT.
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