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∠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°
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°
Answers
GPT-4o mini
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:
**\( m\angle OMN = m\angle LMN - m\angle LMO \)**.
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:
**\( m\angle OMN = m\angle LMN - m\angle LMO \)**.