Measure of ∠MOP is equals to 71.7°.
" Supplementary angles are those angles whose sum is equals to 180°."
According to the question,
∠MOP = 3x - 3
∠MON = 4x + 9
As ∠MOP and ∠MON has common arm OM.
Therefore, ∠MOP and ∠MON are supplementary angles.
As per definition of supplementary angles we have
∠MON + ∠MOP = 180°
Substitute the value of ∠MOP and ∠MON we get,
4x + 9 + 3x - 3= 180°
⇒7x - 6 = 180°
⇒7x = 174
⇒ x = 24.9 (round off)
Substitute the value of x in measure of ∠MOP we get,
∠MOP = 3(24.9) -3
= 71.7°
Hence, measure of ∠MOP is equals to 71.7°.
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