Just a couple questions. "△ABC△ABC is similar to △QRS△QRS by the AA Similarity...."

[Notsogeo]

Just a couple questions. "△ABC△ABC is similar to △QRS△QRS by the AA Similarity...."

Hello, I read the before you post and I know you really are not supposed to post a whole list. But hear me out. I'm terrible at geometry, I barley pasted my last class and it was a credit recovery geometry class. So I apologize if this is too many I could just really use the help. Please and thank you.
P.s. If anyone would be willing to maybe help me with this subject I'd be very grateful.
1. [FONT=MathJax_Main]△[/FONT][FONT=MathJax_Math-italic]A[/FONT][FONT=MathJax_Math-italic]B[/FONT][FONT=MathJax_Math-italic]C[/FONT][FONT=MathJax_Math-italic]△ABC is similar to [FONT=MathJax_Main]△[/FONT][FONT=MathJax_Math-italic]Q[/FONT][FONT=MathJax_Math-italic]R[/FONT][FONT=MathJax_Math-italic]S[/FONT]△QRS by the [FONT=MathJax_Main]AA Similarity Postulate[/FONT]AA Similarity Postulate ​ . The measure of [FONT=MathJax_Main]∠[/FONT][FONT=MathJax_Math-italic]A[/FONT]∠A is 32º and the measure of [FONT=MathJax_Main]∠[/FONT][FONT=MathJax_Math-italic]S[/FONT]∠S is 102º.[/FONT]
What is [FONT=MathJax_Math-italic]m[FONT=MathJax_Main]∠[/FONT][FONT=MathJax_Math-italic]B[/FONT]m∠B?

2. [FONT=MathJax_Main]△[/FONT][FONT=MathJax_Math-italic]A[/FONT][FONT=MathJax_Math-italic]B[/FONT][FONT=MathJax_Math-italic]C[/FONT][/FONT]
[FONT=MathJax_Math-italic]△ABC is similar to [FONT=MathJax_Main]△[/FONT][FONT=MathJax_Math-italic]X[/FONT][FONT=MathJax_Math-italic]Y[/FONT][FONT=MathJax_Math-italic]Z[/FONT]△XYZ by the ​ [FONT=MathJax_Main]AA Similarity Postulate[/FONT]AA Similarity Postulate ​ . The measure of [FONT=MathJax_Main]∠[/FONT][FONT=MathJax_Math-italic]A[/FONT]∠A is 39º and the measure of[FONT=MathJax_Main]∠[/FONT][FONT=MathJax_Math-italic]C[/FONT]∠C is 24º.[/FONT]
What is [FONT=MathJax_Math-italic]m[FONT=MathJax_Main]∠[/FONT][FONT=MathJax_Math-italic]Y[/FONT]m∠Y?

3. [FONT=MathJax_Main]△[/FONT][FONT=MathJax_Math-italic]A[/FONT][FONT=MathJax_Math-italic]B[/FONT][FONT=MathJax_Math-italic]C[/FONT][/FONT]
[FONT=MathJax_Math-italic]△ABC is similar to [FONT=MathJax_Main]△[/FONT][FONT=MathJax_Math-italic]L[/FONT][FONT=MathJax_Math-italic]M[/FONT][FONT=MathJax_Math-italic]N[/FONT]△LMN by the ​ [FONT=MathJax_Main]AA Similarity Postulate[/FONT]AA Similarity Postulate ​ . The measure of [FONT=MathJax_Main]∠[/FONT][FONT=MathJax_Math-italic]A[/FONT]∠A is 129º and[FONT=MathJax_Math-italic]m[/FONT][FONT=MathJax_Main]∠[/FONT][FONT=MathJax_Math-italic]C[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Math-italic]m[/FONT][FONT=MathJax_Main]∠[/FONT][FONT=MathJax_Math-italic]M[/FONT][FONT=MathJax_Main])[/FONT]m∠C=2(m∠M).[/FONT]
What is [FONT=MathJax_Math-italic]m[FONT=MathJax_Main]∠[/FONT][FONT=MathJax_Math-italic]M[/FONT]m∠M?


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[Notsogeo]

I have

Yes I know that and yes I've googled it. But how ever they do not state good instructions on the steps of how to do these. If that was the case I wouldn't be asking.

 

[ksdhart2]

Alright, so we have three problems that are basically the same, but with different numbers. The AA similarity postulate says:

Angle-angle similarity. When two triangles have corresponding angles that are congruent as shown below, the triangles are similar.

So, let's work through each problem and see what information we can glean from this postulate. For each problem, I'd begin by drawing the two similar triangles and fill in information as you go along. If you need a refresher on similar triangles, you might try this page on Math Open Reference.

1) △ABC is similar to △QRS by the AA Similarity Postulate. The measure of ∠A is 32º and the measure of ∠S is 102º. What is m∠B?

You're given the measures of angle A and angle S, so put that information in your picture. Now, because of the AA similarity postulate, knowing the measure of angle A gives you the measure of angle Q. What is it's measure? Why? You also then know the measure of angle C. What is its measure? Why? Now that you have two angles in △ABC, and you also know that the three angles must add up to 180 degrees, what must be the measure of angle B?

2) △ABC is similar to △XYZ by the ​AA Similarity Postulate. The measure of ∠A is 39º and the measure of∠C is 24º. What is m∠Y

You're given the measures of angle A and angle C, so put that information in your picture. From this, you also know the measure of angle B. What is its measure? Why? The problem tells you that △ABC and △XYZ are similar. What does that mean about the angle measures of △XYZ?

3) △ABC is similar to △LMN by the ​AA Similarity Postulate. The measure of ∠A is 129º and m∠C=2(m∠M). What is m∠M?

You're given the measure of angle A, so put that information in your picture. From this, you also know the measure of angle L. What is its measure? Why? Now, if we temporarily denote the measure of angle M as x, we know that the measure of angle C is 2x. What does that make the measure of angle N, in terms of x? The three angles in △LMN must add up to 180 degrees. Two of them are known in terms of x, and one is known outright. Can you set up and solve an equation to find the value of x? Because we declared earlier that the measure of angle M is x, that's your answer to the problem.