Answer: Choice A) Alternate exterior angles are congruent
This is due to the alternate exterior angles theorem.
A more in depth answer would involve a multiple number of paths to take. One such path could have us noticing the following two properties
- angle 1 = angle 4
- angle 8 = angle 5
Both congruences are due to the vertical angle theorem.
Furthermore,
angle 4 = angle 5
because they are alternate interior angles
Then by the transitive property, we effectively connect the dots or the chain links to get to angle 1 = angle 8. We can also use the substitution property as well.
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Side note: angles 1 and 8 are outside the parallel lines 'a' and m, so they are considered exterior angles. Also, they are on alternating sides of the transversal line t. These two facts lead to angles 1 and 8 being alternate exterior angles.
