Urgent Help Please: "The math club designed a pennant for the school team, in the shape of an isosceles triangle."

[MathHelpPlease7171]

I don't understand how to solve this problem, help?
The math club at Tucson High designed a pennant for the school team. The pennant was in the shape of an isosceles triangle. Two points, P and Q, are located so that AC = AP = PQ = QB. Find the measure of angle B. You must show
calculations to support your angle measure.

 

[stapel]

I don't understand how to solve this problem, help?
The math club at Tucson High designed a pennant for the school team. The pennant was in the shape of an isosceles triangle. Two points, P and Q, are located so that AC = AP = PQ = QB. Find the measure of angle B. You must show
calculations to support your angle measure.

What are the points [imath]A[/imath], [imath]B[/imath], and [imath]C[/imath]?

When you reply, please include a clear listing of your thoughts and efforts so far, so that we can see where things are going sideways. ("Read Before Posting")

 

[Harry_the_cat]

Were you given a diagram at all?

 

[The Highlander]

I suspect you may have been given a diagram similar to this...

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Yes?

If so, then you should see that the pink, green & blue triangles are all isosceles too.

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If you then label the internal vertices (I have used the letters \(\displaystyle r\) to \(\displaystyle z\)) something like this...

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... then you can start to form equations like: [math]r+s+t=180\\u+v+w=180\\x+y+z=180\\and, of course,\\r+y+z=180\\note also that...\\x+v+t=180\\and\\s+u=180[/math]
You are tasked with finding the measure of \(\displaystyle \angle{r}\)

As you have isosceles triangles. the base angles are equal and (since for any triangle) any angle is 180 - the sum of the other two, you can also form equations like this...[math]r=180-(y+z)\\r=180-2y\\r=180=2z\\and, since\\s=180-2r\\then\\2r=180-s\\and so on[/math]
Please now come back and show us what equations you might use to solve for a value of \(\displaystyle r\).
Remember: you need two different equations to solve for two unknowns and three equations to solve for three unknowns; note that \(\displaystyle v=180-2u\) is just the same equation as \(\displaystyle 2u=180-v\) (it has just been rearranged ).

Hope that helps.