Question

In the diagram below, m_MON = 1249, m _ MOP = 2x + 1, and m2 NOP = 2x

+1. What are the exact measures of the angles?
N
A. m2 MOP= 62
m2 NOP = 62
B. m2 MOP = 61
m 2 NOP = 61
C. m MOP = 48
m2 NOP = 72
D. m2 MOP = 122
m 2 NOP = 122

Answer 1

The answer is below

Explanation:

The Angle Addition Postulate states that the measure of an angle formed by two or more angles which are placed side by side is the sum of the measures of the two angles.

Therefore:

∠MON = ∠MOP + ∠NOP (angle addition postulate)

Substituting values gives:

124 = (2x + 1) + (2x + 1)

124 = 2x + 2x + 1 + 1

124 = 4x + 2

subtracting 2 from both sides of the equation:

124 - 2 = 4x + 2 - 2

4x = 122

Dividing through by 4:

4x / 4 = 122 / 4

x = 30.5

Therefore ∠MOP = 2x + 1 = 2(30.5) + 1 = 62°, ∠NOP = 2x + 1 = 2(30.5) + 1 = 62°

∠MOP = 62°, ∠NOP = 62°