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.
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.
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.
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