Answer:
∠2 = ∠4 = ∠6 = ∠8 = 114°
∠1 = ∠3 = ∠5 = ∠7 = 66°
Explanation:
You want to know the measures of all of the angles where transversal t crosses parallel lines m and n. ∠4 is given as 114°.
Congruent angles
Where a transversal crosses parallel lines, all of the acute angles are congruent, and all of the obtuse angles are congruent. The obtuse and acute angles form linear pairs, so are supplementary.
In the given figure, the acute angles are numbered using odd numbers, and the obtuse angles are numbered using even numbers.
∠2 = ∠4 = ∠6 = ∠8 = 114°
∠1 = ∠3 = ∠5 = ∠7 = 180° -114° = 66°