Question

m∠LMN
is 46°
, and contains adjacent angles LMO
and OMN
. m∠LMO=22°
. Which statement is true about the relationship of the angles?(1 point)
Responses

m∠OMN=m∠LMN−m∠LMO
.
angle upper O upper M upper N equals angle upper L upper M upper N minus angle upper L upper M upper O .

m∠OMN
is half of m∠LMN
.
angle upper O upper M upper N is half of angle upper L upper M upper N .

m∠LMN<m∠LMO
.
angle upper L upper M upper N less than angle upper L upper M upper O .

m∠OMN +m∠LMN =180°
.

Answer 1

To solve for the relationship of the angles, we start with the given measurements:

- m∠LMN = 46°
- m∠LMO = 22°

Since angles LMO and OMN are adjacent angles, we can find the measure of angle OMN by subtracting the measure of angle LMO from the measure of angle LMN.

Let's calculate m∠OMN:

\[ m∠OMN = m∠LMN - m∠LMO \]
\[ m∠OMN = 46° - 22° \]
\[ m∠OMN = 24° \]

Now, let's evaluate the options provided:

1. **m∠OMN = m∠LMN - m∠LMO**
- This is true since we calculated m∠OMN = 24°.

2. **m∠OMN is half of m∠LMN**
- m∠OMN = 24° and m∠LMN = 46°, and 24° is not half of 46°.

3. **m∠LMN < m∠LMO**
- m∠LMN (46°) is not less than m∠LMO (22°).

4. **m∠OMN + m∠LMN = 180°**
- m∠OMN (24°) + m∠LMN (46°) = 70°, which is not equal to 180°.

The first statement is the **true** one. Thus:

**m∠OMN = m∠LMN − m∠LMO** is the correct answer.