Question

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

m2 = WHAT °.
m3 = WHAT°.
m4 = WHAT °.
m5 = WHAT °.
m6 = WHAT °.
m7 = WHAT °.
m8 = °.


And the second question i have is the picture with words. the other picture is for the question above. Thanks!

Answer 1

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

Answer 2

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.