Answer:
[tex]\bold{\angle NLM = 10^\circ}[/tex]
Step-by-step explanation:
Given a ΔLMN.
Line LN is extended to point O.
such that:
[tex]\text{m}\angle MNO = (5x-13)^{\circ}[/tex]
[tex]\text{m}\angle NLM = (x-4)^{\circ}[/tex] and
[tex]\text{m}\angle LMN = (2x+19)^{\circ}[/tex]
To find:
[tex]\text{m}\angle NLM=?[/tex]
Solution:
Kindly refer to the attached image for the given triangle and dimensions of angles.
Let us recall the external angle property of a triangle:
The external angle of a triangle is equal to the sum of two opposite internal angles.
i.e.
[tex]\angle MNO = \angle NLM + \angle LMN\\\Rightarrow 5x-13 = x-4+2x+19\\\Rightarrow 5x-13 = 3x+15\\\Rightarrow 5x-3x = 13+15\\\Rightarrow 2x=28\\\Rightarrow x =14[/tex]
Putting the value of [tex]x[/tex] in [tex]\angle NLM[/tex].
[tex]\angle NLM=14-4 \\\Rightarrow \bold{\angle NLM = 10^\circ}[/tex]
