Answer:
Step-by-step explanation:
Let's start by identifying relevant angle theorems for two parallel lines cut by a transversal.
Alternate Interior Angles Theorem
Two angles that are on different sides of the transversal and inside of the two parallel lines are congruent (=).
Alternate Exterior Angles Theorem
Two angles that are on different sides of the transversal and outside of the two parallel lines are congruent (=).
Same-side Interior Angles Theorem
Two angles that are on the same side of the transversal and inside of the two parallel lines are supplementary (= 180).
Same-side Exterior Angles Theorem
Two angles that are on the same side of the transversal and outside of the two parallel lines are supplementary (=180).
Corresponding Angles Theorem
Two angles on a figure that correspond are congruent (=).
_
Now, let's look at the figure and apply these theorems.
and
are same-side exterior angles, meaning they're supplementary:
Subtract from both sides of the equation:
Now that we know our value, let's recognize that
(
)corresponds to
, meaning they're congruent:
Subtract from both sides of the equation:
Let's find the value of the angle:
Add:
Since the corresponding angles are of the same value, they're congruent, proving our &
values correct.
_
Since and the angle represented by the expression
(
°) are alternate-interior angles, they are congruent: