∠A and ∠B are opposite interior angles, which means they are equal to each other. Make them equal to each other in an equation.
∠A = ∠B ⇒ 5x - 12 = 2x + 24
Add 12 to both sides.
5x = 2x + 36
Subtract 2x from both sides.
3x = 36
Divide both sides by 3.
x = 12
Now plug x into the equation for ∠B.
2x + 24 ⇒ 2(12) + 24 = 48
∠B = 48°
