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Answer:
angles 1-8 are 62°, 71°, 109°, 35°, 109°, 29°, 47°, 62°
Step-by-step explanation:
It is convenient to make use of the relations ...
- an exterior angle of a triangle is equal to the sum of the remote interior angles
- vertical angles are congruent
- a linear pair is supplementary
- at a transversal of parallel lines, alternate interior angles are congruent
- at a transversal of parallel lines, adjacent interior angles are supplementary
Using these relations, we have ...
∠2 = 71° (vertical angles)
∠3 = ∠5 = 180° -71° = 109°
∠1 +47° = ∠3 = 109° ⇒ ∠1 = ∠8 = 62° (alt int angles)
∠4 +36° = 71° ⇒ ∠4 = 35°
∠6 +42° = ∠2 = 71° ⇒ ∠6 = 29°
∠7 = 47° (alt int angles)
There are other ways to work these, using the sum of angles in a triangle, for example.
In order, angles 1-8 are ...
62°, 71°, 109°, 35°, 109°, 29°, 47°, 62°
