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
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∠OMN +m∠LMN =180°

Answer 1

To solve this problem, we need to analyze the information given about the angles \( \angle LMN \), \( \angle LMO \), and \( \angle OMN \).

1. Given Information:

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

2. Finding \( m\angle OMN \):

   • Since \( LMO \) and \( OMN \) are adjacent angles that together form \( \angle LMN \): \[ m\angle LMN = m\angle LMO + m\angle OMN \]
   • Substituting the known values: \[ 46^\circ = 22^\circ + m\angle OMN \]
   • To find \( m\angle OMN \), we subtract \( 22^\circ \) from \( 46^\circ \): \[ m\angle OMN = 46^\circ - 22^\circ = 24^\circ \]

3. Now, evaluate the given statements:

   • Statement 1: \( m\angle LMN < m\angle LMO \)

     • This is false because \( 46^\circ > 22^\circ \).

   • Statement 2: \( m\angle OMN \) is half of \( m\angle LMN \)

     • \( m\angle OMN = 24^\circ \) which is not half of \( 46^\circ \) (half would be \( 23^\circ \)). This statement is false.

   • Statement 3: \( m\angle OMN = m\angle LMN − m\angle LMO \)

     • We calculated \( m\angle OMN = 24^\circ \) and confirmed that: \[ m\angle LMN - m\angle LMO = 46^\circ - 22^\circ = 24^\circ \]
     • This statement is true.

   • Statement 4: \( m\angle OMN + m\angle LMN = 180^\circ \)

     • \( m\angle OMN + m\angle LMN = 24^\circ + 46^\circ = 70^\circ \), which is not equal to \( 180^\circ \). This statement is false.

The only true statement about the relationship of the angles is:

\( m\angle OMN = m\angle LMN - m\angle LMO \).