Question

Angles LMN and OMP have the following measures:

m∠LMN = (x + 12)°, m∠OMP = (4x − 7)°

If angle LMN and angle OMP are complementary angles, find the value of x.

Use the value of x from Part A to find the measures of angles LMN and OMP.

Could the angles also be vertical angles? Explain.

1. The value of x will be equal to 35, the angle LMN will be equal to 47° and the angle OMP will be equal to 133°

### What is a complementary angle?

By adding up the two anglesmeasurements, one can determine the complement and supplement of the two angles. Complementary angles are those where the summation of angles equals the measurements of a right angle.
A)
The complementary angle means that the sum of angles will be 180°.
The given angles are : ∠LMN = (x + 12)° and ∠OMP = (4x − 7)°.
(x +12) + (4x – 7) = 180°
5x + 5 = 180
5x = 175
x = 175/5
x=35°
B)
Substitute x=35° for the first angle,
35+12
LMN = 47°
Substitute x=35 for the second angle,
4(35)-7
OMP = 133°
To know more about complementary angles:
#SPJ2

2. nguyetanh

A)
Complementary means it adds to 180.
You have to set the two angles equal to 180 like so:
x+12+4x-7=180
Simplify
5x+5=180
5x=175
x=35
B)
Plug the value of X into the Two angles and solve:
35+12
=47 For angle one
4(35)-7
=133