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

41

67

113

139
Can someone please explain to me how to do this?

Quadrilateral OPQR is inscribed in circle N, as shown below. What is the measure of ROP? 41 67 113 139 Can someone please explain to me how to do this? class=

Verified Answer :

W0lf93

We should know that the sum of the interior
angles or an irregular polygon must be equal to 360°.
For examples, the case of
a square: 90° +90°+90°+90°=360°.
So in our case, the sum of the angles is
Sum=360°= (x+17)°+(2x+9)°+ (6x-5)° + meas OPQ,
it implies measOPQ=360°-(x+17)° - (2x+9)° - (6x-5)°
=360°-9x -31°=(329-9x)°

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