Respuesta :

Answer:

Option A is correct.

The value of m is, 10.

Step-by-step explanation:

From the figure;

The line through the points L, H, and J is a straight line.

Since the [tex]\angle LHM[/tex] and [tex]\angle JHM[/tex] 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: [tex]\angle LHM =(2m+10)^{\circ}[/tex] and [tex]\angle JHM=(5m+100)^{\circ}[/tex]

Then,

[tex]\angle LHM+\angle JHM =180^{\circ}[/tex]

⇒ [tex]2m+10+5m+100 =180[/tex]

Like terms are those terms which are of same variable.

Now, combine like terms;

[tex]7m+110=180[/tex] or

[tex]7m= 180-110[/tex]

Simplify:

[tex]7m=70[/tex]

Divide 7 both sides, we get

[tex]\frac{7m}{7}= \frac{70}{7}[/tex]

Simplify:

m=10.

Therefore, the value of m is, 10


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Use the concept of linear pair of angles. The Correct value of m is 10.

We first need to check like terms and then we will simplify accordingly.

Given:

The line where, the points L, H, and J is a straight line.

We know that according to the given figure,

[tex]\rm \angle LHM = (\rm 2m+10)\textdegree\\ \angle JHM=(5m +100)\textdegree[/tex]

∠LHM &; ∠JHM forms a linear pair,

What is linear pair?

A linear pair is given in the figure the two angles which are adjacent to one another and they form a straight line.

If any two angles form a linear pair then they are making supplementary.

Now, we know that

[tex]\rm \angle LHM = (\rm 2m+10)\textdegree\\ \angle JHM=(5m +100)\textdegree[/tex]

Now,

[tex]\rm We\; knows \;that \;supplementary \;angle = 180 \textdegree\\\rm\angle LHM + \angle JHM =180\textdegree\\\\2m+10+5m+100=180 \textdegree[/tex]

Those terms which are of the same variables are called like terms.

On solving further we get,

[tex]\rm 7m+110=180\textdegree\\7m= 180\textdegree -110\textdegree\\7m=70\textdegree\\\\Now\;we \;divide\;both \;the\;side\;with7\\\\\dfrac{7m}{7}= \dfrac{70}{7}\\\\m=10[/tex]

Therefore, the Correct value of m is 10.

Learn more about Supplementary angles here: https://brainly.com/question/21504800

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