1) You have the following expressions for angles ∠1 and ∠3
m∠1 = 15x - 5
m∠3 = 10x + 35
In order to find the value of x, you consider that angle ∠1 and ∠3 are congruent, that is, they are equal. Then, you equal the algebraic expressions and solve for x, just as follow:
15x - 5 = 10x + 35 subtract 10x bith sides, add 5 both sides
15x - 10x = 35 + 5 simplify similar terms
5x = 40 divide between 5 both sides
x = 40/5
x = 8
Hence, x = 8, and the values of the angles are:
m∠1 = 15x - 5 = 15(8) - 5 = 115
m∠3 = 10x + 35 = 10(8) + 35 = 115
2) To find the measure of the angle ∠2 you consider that the sum of angles ∠1 and ∠2 is equal to 180°. Thus, you obtain:
m∠1 + m∠2 = 180°
m∠2 = 180 - m∠1 = 180 - 115 = 65
Hence, the measure of angle m∠2 = 65°