Question

In the figure below, m || n and t is a transversal line. If ∠7 = x +14 and ∠1 = 2x -8, what is ∠4?

Answer 1

∠4 and ∠1 are opposite angles, and since opposite angles are equal, ∠4 =  2x - 8

(if u need a specific number)

∠1 is corresponding to ∠5, and since corresponding angles are equal, ∠5 = 2x-8

∠7 is supplementary to ∠5, and since supplementary angles add up to 180, x + 14 + 2x - 8 = 180

-> 3x + 6 = 180
x = (180-6)/3 = 58.

Since ∠4 = 2x - 8 -> ∠4 = 2 x 58 - 8 = 108.