140° + ∠5 = 180° same side interior angles ⇒ ∠5 = 40°
∠2 ≅ ∠5 vertical angles ⇒ ∠2 = 40°
∠8 = 53° alternate interior angles
∠3 ≅ ∠8 vertical angles ⇒ ∠3 = 53°
x + ∠2 + ∠3 = 180° triangle sum theorem
x + 40° + 53° = 180°
x + 93° = 180°
x = 87°
Answer: 87°
Note: I just realized that there is an easier way to solve this:
∠9 + 53° + x = 180° triangle sum theorem
140° + ∠9 = 180° supplementary angles ⇒ ∠9 = 40°
40° + 53° + x = 180°
x + 93° = 180°
x = 87°
Use whichever solutions makes sense to you.
