Question

m∠LMN=m∠NMO m, angle, N, M, O, equals, one half, left bracket, m, angle, L, M, N, right bracket\text{m}\angle NMO=\frac{1}{2}\left(\text{m}\angle LMN\right)m∠NMO= 2 1 ​ (m∠LMN) m, angle, L, M, N, equals, m, angle, L, M, O\text{m}\angle LMN= \text{m}\angle LMOm∠LMN=m∠LMO m, angle, L, M, O, equals, 2, left bracket, m, angle, N, M, O, right bracket\text{m}\angle LMO= 2\left(\text{m}\angle NMO\right)m∠LMO=2(m∠NMO)

Answer 1

1. m∠LMN = m∠NMO (Given)
2. m∠NMO = (1/2) * m∠LMN (Given)
3. m∠LMN = m∠LMO (Given)
4. m∠LMO = 2 * m∠NMO (Given)

Now, we can use these equations to find the relationship between the angles:

From equations 1 and 2:
m∠LMN = m∠NMO
m∠NMO = (1/2) * m∠LMN

Now, substitute m∠LMN from equation 1 into equation 4:
m∠LMO = 2 * m∠NMO
m∠LMO = 2 * [(1/2) * m∠LMN]
m∠LMO = m∠LMN

So, we have found that m∠LMO = m∠LMN, which means that the angle at point M is the same regardless of whether you look at it from points N or O.