The measure of angle NMQ is 73 degrees
The given parameter is:
[tex]\angle MNP = 107[/tex]
From the given figure, angles MNP and NMQ are adjacent angles.
Given that the adjacent angles of a trapezoid add up to 180 degrees.
We have the following equation
[tex]\angle MNP + \angle NMQ = 180[/tex]
Make NMQ the subject
[tex]\angle NMQ = 180 -\angle MNP[/tex]
Substitute 107 for MNP
[tex]\angle NMQ = 180 -107[/tex]
[tex]\angle NMQ = 73[/tex]
Hence, the measure of angle NMQ is 73 degrees
Read more about adjacent angles at:
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