Question

List the sides of each triangle from shortest to greatest. Triangle has angles 45, 50, x. How do I find the missing angle? I know the triangle inequality theorem, but I'm confused on how to get a straight answer.

Answer 1

Given a triangle with angle measures a, b and c degrees,

then a+b+c = 180°.

This is always true.

So:

45°+50°+x°=180°
95°+x°=180°
x°=180°-95°=85°

So the measure of the missing angle is 85°.

Thus x>50°>45°

Another important theorem is that the angle measures and the lengths of the sides opposite these angles are directly proportional,

that is, the larger side is opposite the larger angle.

Answer:

(side length opposite) x> (side length opposite) 50°> (side length opposite) 45°