What is the value of m

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)

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and \angle JHM=(5m+100)^{\circ}∠JHM=(5m+100)

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Then,

\angle LHM+\angle JHM =180^{\circ}∠LHM+∠JHM=180

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⇒ 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