Question

List the sides of ΔABC in order from shortest to longest, when m∠A = 10x – 7, m∠B = 7x – 10, and m∠C = 47 – 2x.

Answer 1

m<A + m<B + m<C = 180


(10x-7) + (7x-10) + (47-2x) = 180


10x-7 + 7x-10 + 47-2x = 180


(10x+7x-2x) + (-7-10+47) = 180


15x + 30 = 180


15x + 30-30 = 180-30


15x = 150


15x/15 = 150/15


x = 10


So


m<A = 10x-7 = 10(10)-7 = 93 degree

m<B = 7x – 10 = 7(10)-10 = 60 degrees

m<C = 47 – 2x = 47-2(10) = 27 degrees


Therefore, the side BC is the longest (since it's opposite angle A, which is the largest angle), followed by side AC (it's opposite angle B) and finally side AB is the shortest


A pic might help see this.

Answer 2

this helps alot man! thanks