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

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∠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 determine the correct statement about the relationship between the angles, we can use the information provided:

1. \( m∠LMN = 46° \)
2. \( m∠LMO = 22° \)

To find \( m∠OMN \), we can use the fact that the sum of the angles in a straight line is 180°:

\[
m∠LMN = m∠LMO + m∠OMN
\]

This can be rewritten to solve for \( m∠OMN \):

\[
m∠OMN = m∠LMN - m∠LMO
\]

Now substituting the known values:

\[
m∠OMN = 46° - 22° = 24°
\]

Now let's evaluate the provided statements:

1. **m∠OMN is half of m∠LMN.**
- \( m∠OMN = 24° \) and \( \frac{1}{2} m∠LMN = \frac{1}{2} \times 46° = 23° \). This statement is false.

2. **m∠OMN = m∠LMN - m∠LMO.**
- As calculated, \( m∠OMN = 46° - 22° = 24° \). This statement is true.

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

4. **m∠OMN + m∠LMN = 180°.**
- \( 24° + 46° = 70° \). This statement is false.

Thus, the correct statement is:

**m∠OMN = m∠LMN - m∠LMO.**