Answer:
x = 45°
y = 135°
Step-by-step explanation:
Hi, Ace here!
Over here, we have a transversal with m parallel to n. Because those two lines are parallel, we can apply many theorems to this transversal.
First, we can say that m<45° and m<x° are corresponding angles. According to this theorem, that means both these degree measures are equal, thus x = 45°.
To find y, we can do 1 of two things in 1 step. We can name m<45° and m<y° as same side exterior angles, which means that they'd be supplementary angles (add up to 180°).
The second thing we can do is say m<x and m<y supplement each other because the measure of a flat line equals 180°, and according to Part-Whole-Postulate, that means all the parts of the flat line would also equal up to 180°.
Of course, these methods are practically the same due to substitution (m<x=m<45°). So m<y = 180° - m<x or m<y = 180° - 45° = 135°.
Hope this helped, let me know if you have any questions.
