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∠1 and ∠2 are supplementary angles. ∠1 and ∠3 are vertical angles. If m ∠2=72 degrees, then find m ∠3

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Answer:

m<3 = 108

Step-by-step explanation:

Since <1 and <2 are supplementary, the equation is:

<1 + <2 = 180

Since <1 and <3 are vertical angles. the equation is:

<1 = <3

To find m<3:

<2 + <3 = 180

72 + <3 = 180

<3 = 180 - 72

<3 = 108

The measure of angle ∠3 is 108 degrees.

What is supplementary angle?

Supplementary angles are those angles that sum up to 180 degrees. They don't have to be next to each other, just so long as the total is 180 degrees.

What is vertical angle?

Vertical angles are formed when two lines meet each other at a point. They are always equal to each other.

For the given situation,

∠1 and ∠2 are supplementary angles.

∠1 and ∠3 are vertical angles.

Measure of angle, m ∠2 = 72

From definition, we know that

∠1 + ∠2 = 180 (supplementary angles) ------- (1)

and

∠1 = ∠3 (vertical angles) --------- (2)

From (1) and (2),

⇒ [tex]\angle3 + \angle2 = 180[/tex]

⇒ [tex]\angle3=180-72[/tex]

⇒ [tex]\angle3=108[/tex]

Hence we can conclude that the measure of angle ∠3 is 108 degrees.

Learn more about measurement of angles here

https://brainly.com/question/3027144

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