Question

Find the measure of each angle. Assume the lines are parallel.

Answer 1

Answer:

Givens

$\angle 1 = 113\°$

In the image provided we have a pair of parallels lines and a transversal, this setup forms 8 angles which are related in pairs.

Therefore,

$\angle 2= 180\° - 113\° = 67\°$, by supplementary angles defintion.

$\angle 3 = \angle 1 = 113 \°$, by corresponding angles definition.

$\angle 4 = \angle 2 = 67\°$, by supplementary angles.

$\angle 5 = \angle 1 = 113\°$, by alternate exterior angles.

$\angle 6 = \angle 2 = 67\°$, by alternate exterior angles.

$\angle 7 = \angle 1 = 113\°$, by vertical angles definition.

$\angle 8 = \angle 2 = 67\°$, by vertical angles.

The answer to the second question is 76°, that's the value that makes lines a and b parallel, because that way those angles would be alternate interior angles, which are always congruent when they are formed by a pair of parallels and a transversal.

Answer 2

2=67 degrees
3=113 degrees
4=67 degrees
5=113 degrees
6=67 degrees
7=113 degrees
8=67 degrees