I don’t know how to navigate your site yet, so please forgive me if you have already answered this question. Regarding question number 8 in your book, will you further explain why y=180-x is the same angle degree as the unmarked angle? I know y=2x because of geometry, but I do not understand how y can also equal x?

You’re talking about this question from the triangles chapter, right?

You’ve actually hit on a totally legit way to solve the question: If due to the exterior angle theorem, and , then you can substitute and solve for :

Once you know that , you can determine that the triangle is equilateral, so you need a perimeter that’s a multiple of 3.

To answer your question more directly, look at just the top part of the figure:

See how you’ve got a straight line there? That means the angle that’s NOT marked (i.e., the angle inside the triangle) has a measure of . Since the question tells you that , you can substitute: