Answer:
m∠1 = 54°
m∠3 = 105°
Explanation:
The sum of the measures of the complementary angles is 90°
The sum of the measures of the supplementary angles is 180°
∵ ∠1 is a complement of ∠2
∴ m∠1 + m∠2 = 90°
∵ m∠2 = 36°
→ Substitute it in the rule above
∴ m∠1 + 36 = 90
→ Subtract 36 from both sides
∴ m∠1 + 36 - 36 = 90 - 36
∴ m∠1 = 54°
∵ ∠3 is a supplement of ∠4
∴ m∠3 + m∠4 = 180°
∵ m∠4 = 75°
→ Substitute it in the rule above
∴ m∠3 + 75 = 180
→ Subtract 75 from both sides
∴ m∠3 + 75 - 75 = 180 - 75
∴ m∠3 = 105°