Answer :

You have the following expressions for two angles of the given figure.

∠1 = 7x - 4

∠2 = 3x + 28

Such angles are generated by a secant line which crosses two parallel lines. Furthermore, these angles are congruent, which means that their measures are equal.

Then, you equal both given expressions and solve for x, just as follow:

7x - 4 = 3x + 28 subtract 3x both sides

7x - 3x - 4 = 28 add 4 both sides

7x - 3x = 28 + 4 simplify like terms

4x = 32 divide by 4 both sides

x = 32/4

x = 8

Hence, the value of x is x = 8