m∠LMN

Question

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

m∠OMN +m∠LMN =180°
.
angle upper O upper M upper N plus angle upper L upper M upper N equals 180 degrees .

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
.

Answer 1

To analyze the given angles, we know the following:

• \( m\angle LMN = 46^\circ \)
• \( m\angle LMO = 22^\circ \)

Since angles \( LMO \) and \( OMN \) are adjacent to angle \( LMN \), we can find \( m\angle OMN \) by using the relationship between the angles:

\[ m\angle LMN = m\angle LMO + m\angle OMN \]

Substituting the values we have:

\[ 46^\circ = 22^\circ + m\angle OMN \]

To find \( m\angle OMN \):

\[ m\angle OMN = 46^\circ - 22^\circ = 24^\circ \]

Now we can evaluate each of the response statements:

1. m∠LMN < m∠LMO:
   \( 46^\circ < 22^\circ \) is false.

2. m∠OMN + m∠LMN = 180°:
   \( 24^\circ + 46^\circ = 70^\circ \), not \( 180^\circ \). This statement is false.

3. m∠OMN is half of m∠LMN:
   \( 24^\circ \) is not half of \( 46^\circ \) (half of \( 46^\circ \) is \( 23^\circ \)). This statement is false.

4. m∠OMN = m∠LMN - m∠LMO:
   \( 24^\circ = 46^\circ - 22^\circ \) is true.

The correct statement is:

m∠OMN = m∠LMN - m∠LMO.