Well, m∠1 and m∠3 are congruent by the Vertical Angle Congruent Theorem (VACT). This means that because the angles are opposite of each other, their angles are the same because they are formed by the same two intersecting lines.
Because of this, we can set m∠1 and m∠3 equal to each other:
m∠1 = m∠3
(2x + 28) = (6x + 4)
2x + 28 = 6x + 4
-4x + 28 = 4
-4x = -24
-x = -6
x = 6
Knowing that x equals 6, we can use this to find m∠2. By the Supplementary Angles Theorem (SAT), angles that are on the same line add up to equal 180°. To use the SAT, we need to plug x in to find m∠1 or m∠3, because they are both the same:
x = 6
m∠1 = (2x + 28)
m∠1 = 2(6) + 28
m∠1 = 12 + 28
m∠1 = 40°
m∠3 also equals 40°.
Now that we have the value for ∠1 (or ∠3), we can use the SAT:
m∠2 + m∠3 = 180 ← You could also use m∠1, because they both equal the same!
m∠2 + 40 = 180
m∠2 = 140°
So, the measure of ∠2 is 140°.
If you have any questions, feel free to ask! :)
