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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°

1 answer

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.