Given: m∠MON = 135°
If ∠MOL and ∠MON are supplementary angles, then what is the measure of ∠NOP?
If two angles are supplementary angles, then the sum of their measures is 180 degrees.
Since ∠MOL and ∠MON are supplementary angles, we can write:
m∠MOL + m∠MON = 180°
Since we know that m∠MON = 135°, we can substitute this value into the equation:
m∠MOL + 135° = 180°
Now, we can solve for m∠MOL by subtracting 135° from both sides:
m∠MOL = 180° - 135°
m∠MOL = 45°
So, the measure of ∠MOL is 45 degrees.
Since ∠NOP is vertical to ∠MOL, they have equal measures.
Therefore, the measure of ∠NOP is also 45 degrees.