Final answer:
To find m∡NMO, add m∡NMP and m∡OMP, set their sum equal to 180°, solve for x, and substitute back into either angle. The measure of m∡NMO is approximately 96°.
Step-by-step explanation:
To find the measure of angle NMO (m∡NMO), you must understand that NMO is a straight line and therefore the sum of angles NMP and OMP that form a straight line is 180°.
First, we must set up an equation acknowledging that the sum of the angles on the straight line is equal to 180°:
m∡NMP + m∡OMP = 180°
(3x + 8)° + (4x - 6)° = 180°
Solving for x:
3x + 4x + 8 - 6 = 180
7x + 2 = 180
7x = 178
x = 178 / 7
x = 25.4286...
Now we can find the m∡NMO by substituting the value of x back into either m∡NMP or m∡OMP:
Let's substitute x into m∡OMP (4x - 6)°:
m∡OMP = (4(25.4286) - 6)°
m∡OMP = (101.7144 - 6)°
m∡OMP = 95.7144°
Hence, m∡NMO = 95.7144°, or approximately 96° when rounded to the nearest whole number.