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Given that m∠nmp=(3x 8)° and m∠omp=(4x-6)° , identify m∠nmo ?

User Evil Trout
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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.

User Rui Lopes
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