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 y=2x due to the exterior angle theorem, and y=180-x, then you can substitute and solve for x:


Once you know that x=60, 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 y^\circ (i.e., the angle inside the triangle) has a measure of (180-y)^{\circ}. Since the question tells you that y=180-x, you can substitute:



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