Given: m∠NRQ = 165°
If ∠NRO and ∠NRQ are supplementary angles, then what is the measure of ∠PRQ?
If ∠NRO and ∠NRQ are supplementary angles, that means they add up to 180°. So, ∠NRO = 180° - ∠NRQ = 180° - 165° = 15°.
Since ∠PQR is a straight angle and ∠NRQ is an angle on the same line, they are supplementary angles. Therefore, the measure of ∠PRQ is also 180° - ∠NRQ = 180° - 165° = 15°.