Answer:
Givens
[tex]\angle 1 = 113\°[/tex]
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,
[tex]\angle 2= 180\° - 113\° = 67\°[/tex], by supplementary angles defintion.
[tex]\angle 3 = \angle 1 = 113 \°[/tex], by corresponding angles definition.
[tex]\angle 4 = \angle 2 = 67\°[/tex], by supplementary angles.
[tex]\angle 5 = \angle 1 = 113\°[/tex], by alternate exterior angles.
[tex]\angle 6 = \angle 2 = 67\°[/tex], by alternate exterior angles.
[tex]\angle 7 = \angle 1 = 113\°[/tex], by vertical angles definition.
[tex]\angle 8 = \angle 2 = 67\°[/tex], 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.
