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.
