Question

Help solve for x please (ignore my incorrect math)

Answer 1

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.