Answer:
A) x = 44
B) m∠1 = 118°
m∠2 = 62°
Step-by-step explanation:
Part A
Angles on a straight line sum to 180°
⇒ (2x + 30) + 62 = 180
⇒ 2x + 30 + 62 = 180
⇒ 2x + 92 = 180
⇒ 2x = 88
⇒ x = 44
Part B
Vertical Angle Theorem: The opposite vertical angles of two straight intersecting lines are congruent.
⇒ m∠1 = (2x + 30)
Substituting the found value of x:
⇒ m∠1 = 2(44) + 30
⇒ m∠1 = 88 + 30
⇒ m∠1 = 118°
Using the Vertical Angle Theorem:
⇒ m∠2 = 62°
