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
.
measure of angle upper O upper M upper N equals measure of angle upper L upper M upper N minus measure of angle upper L upper M upper O .

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

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

m∠OMN +m∠LMN =180°

Answer 1

To analyze the relationships between the angles, let's summarize the given information:

- m∠LMN = 46°
- m∠LMO = 22°

We can find the measure of angle \( m∠OMN \) using the fact that the angles \( m∠LMO \), \( m∠OMN \), and \( m∠LMN \) are adjacent angles that sum up to \( m∠LMN \).

Using the fact that the angles form a straight line:

\[
m∠LMN = m∠LMO + m∠OMN
\]

Substituting the known values:

\[
46° = 22° + m∠OMN
\]

To find \( m∠OMN \), we can rearrange the equation:

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

Now, let's evaluate the responses:

1. **m∠OMN = m∠LMN - m∠LMO** – This statement is true because \( 24° = 46° - 22° \).

2. **m∠LMN < m∠LMO** – This statement is false since \( 46° > 22° \).

3. **m∠OMN is half of m∠LMN** – This statement is false as \( 24° \) is not half of \( 46° \).

4. **m∠OMN + m∠LMN = 180°** – This statement is false since \( 24° + 46° = 70° \), not \( 180° \).

The correct response is:

**m∠OMN = m∠LMN - m∠LMO**.