Answer:
From the figure;
The line through the points L, H, and J is a straight line.
Since the \angle LHM∠LHM and \angle JHM∠JHM forms a linear pair.
A linear pair is two angles that are adjacent to each other and forms a line.
Also, If two angles form a linear pair then they are supplementary.
Given: \angle LHM =(2m+10)^{\circ}∠LHM=(2m+10)
∘
and \angle JHM=(5m+100)^{\circ}∠JHM=(5m+100)
∘
Then,
\angle LHM+\angle JHM =180^{\circ}∠LHM+∠JHM=180
∘
⇒ 2m+10+5m+100 =1802m+10+5m+100=180
Like terms are those terms which are of same variable.
Now, combine like terms;
7m+110=1807m+110=180 or
7m= 180-1107m=180−110
Simplify:
7m=707m=70
Divide 7 both sides, we get
\frac{7m}{7}= \frac{70}{7}
7
7m
=
7
70
Simplify:
m=10.
Therefore, the value of m is, 10
