Answer:
m∠1 = 75°
m∠2 = 105°
m∠3 = 75°
m∠4 = 105°
Explanation:
Angles on a straight line sum to 180°
⇒ m∠1 + m∠2 = 180°
Given:
⇒ m∠2 - m∠1 + m∠1 = 30° + m∠1
⇒ m∠2 = 30° + m∠1
Substitute the found expression for m∠2 into the first equation and solve for m∠1:
⇒ m∠1 + m∠2 = 180°
⇒ m∠1 + 30° + m∠1 = 180°
⇒ m∠1 + 30° + m∠1 - 30° = 180° - 30°
⇒ m∠1 + m∠1 = 150°
⇒ m∠1 = 150° ÷ 2
⇒ m∠1 = 75°
As angles on a straight line sum to 180°, subtract m∠1 from 180° to find m∠2:
⇒ m∠2 = 180° - m∠1
⇒ m∠2 = 180° - 75°
⇒ m∠2 = 105°
Vertical Angles Theorem: When two straight lines intersect, the opposite vertical angles are the same (congruent).
⇒ m∠3 = m∠1 = 75°
⇒ m∠4 = m∠2 = 105°