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∠OMN +m∠LMN =180°
.
m∠OMN +m∠LMN =180°
. - no response given

m∠OMN
is half of m∠LMN
.
m∠OMN
is half of m∠LMN
. - no response given

m∠OMN=m∠LMN−m∠LMO
.
m∠OMN=m∠LMN−m∠LMO
. - no response given

m∠LMN<m∠LMO
.
m∠LMN<m∠LMO
.

Answer 1

To determine the correct statement about the angles, let's analyze the information provided.

1. You know that \( m∠LMN = 46° \).
2. You also know that \( m∠LMO = 22° \).

To find \( m∠OMN \), we can use the relationship between the angles:

Since \( ∠LMN \) is the sum of \( ∠LMO \) and \( ∠OMN \), we can write the equation:

\[ m∠LMN = m∠LMO + m∠OMN \]

Substituting the known values:

\[ 46° = 22° + m∠OMN \]

Now, we can solve for \( m∠OMN \):

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

With this information, let's evaluate the provided responses:

1. m∠OMN + m∠LMN = 180°: This is not true because \( m∠LMN + m∠OMN = 46° + 24° = 70°\).

2. m∠OMN is half of m∠LMN: This is false because \( m∠OMN = 24°\) which is not half of \( 46°\).

3. m∠OMN = m∠LMN − m∠LMO: This is true because \( m∠OMN = 46° - 22° = 24°\).

4. m∠LMN < m∠LMO: This is false because \( 46° > 22°\).

The correct statement is:

m∠OMN = m∠LMN − m∠LMO.