Question

Please help and explain how you did it

Answer 1

To determine the lengths of the sides from shortest to longest, you need to calculate the corresponding angles. The higher angles will correspond to longer sides.

To find the angles, you have to solve for x. You’re already given that angle A is 76. To find the others, you know that angle C is 180-(16x+16) since it’s supplemental to the exterior angle. Then, you know the sum of the angles of the entire triangle is 180, so add up A, B, and C

A+B+C=180
76+6x+(180-16x-16)=180
240-10x=180
-10x=-60
x=6

So to find angle B, you use 6x or 6(6)=36.

To find angle C, you use 180-(16x-16) or 180-16(6)-16=68

So now match up the angles with their corresponding sides to find the length from shortest to longest.

Angle A (76) corresponds with BC
Angle B (36) corresponds with AC
Angle C (68) corresponds with AB

Again, the higher the degree, the longer the corresponding side, so AC is shortest, AB is next, and BC is the longest.