Answer:
∠1 = ∠4 = ∠5 = ∠8 = 55°
∠2 = ∠3 = ∠6 = ∠7 = 125°
Step-by-step explanation:
Where a transversal (a) crosses parallel lines (c and d), corresponding angles are congruent. Vertical angles are congruent any time.
Here, pairs of corresponding angles are ...
(1, 5), (2, 6), (3, 7), (4, 8)
Pairs of vertical angles are ...
(1, 4), (2, 3), (5, 8), (6, 7)
Together, these tell you ...
∠1 = ∠4 = ∠5 = ∠8 = 55°
Of course, the linear pair ∠1 and ∠2 are supplementary, so ...
∠2 = 180° -∠1 = 125°
Then the congruences listed above tell you ...
∠2 = ∠3 = ∠6 = ∠7 = 125°
