Answer:
m∠1 = m∠3 = 75°
m∠2 = m∠4 = 105°
Step-by-step explanation:
From the figure attached,
m∠1 + m∠2 = 180° [Supplementary angles]------(1)
Since, m∠2 - m∠1 = 30°
m∠2 = 30° + m∠1 -----(2)
By substituting the value of ∠2 from equation (2) to equation (1),
m∠1 + (m∠1 + 30°) = 180°
2(m∠1) + 30° = 180°
2(m∠1) = 150°
m∠1 = 75°
Therefore, m∠2 = 180°- m∠1 = 180° - 75°
m∠2 = 105°
Since, ∠ 2 ≅ ∠4 [Vertical angles]
m∠2 = m∠4 = 105°
Similarly, ∠1 ≅ ∠3 [Vertical angles]
m∠1 = m∠3 = 75°
