Question

In an isosceles triangle LSU with base angles L and S, Angle S is 4 more than one-half the measure of Angle U. Find all three angles.
Note: I need the process of how to do these questions, not just the answer by itself. We keep being assigned these types of problems but so far I haven't figured out how these work.

Answer 1

All you need to do is find one base angle, since in an isosceles triangle, both those angles are opposite equal sides, and are therefore equal.

You can use the Pythagorean Theorem to obtain the altitude (the unknown side in the middle.)

The vertex, B, is split into two equal angles, but you can easily find the vertex angle by first finding one of the base angles.

You can find the base angle B by using the fact that

cosB=AdjacentHypotenuse⟹B=cos−1(AdjacentHypotenuse)=cos−1(10.925.6)=64.8

Each base angle, let's call them each of measure x, plus the vertex angle add up to 180.

So if you need to solve for the vertex angle θ, we have that θ=180−2x.

Also note, to find an angle, given none of the angles are known, you can to use the lengths of the sides of the triangle to solve for the base angles and/or vertex, and can use the Law of Cosines to do that.