Question

lines mn and gh are parallel. if m∠s is 38°, then what is m∠y?
a. 43°
b. 142°
c. 322°
d. 38°

Explanation:

Step1: Identify vertical angle of ∠S

∠S and ∠X are vertical angles, so $m∠X = m∠S = 38^\circ$.

Step2: Use consecutive interior angles theorem

MN || GH, so ∠X and ∠Y are consecutive interior angles (supplementary).
$m∠Y = 180^\circ - m∠X = 180^\circ - 38^\circ = 142^\circ$.

Answer:

B. 142°