Math Is Fun Forum

yeager51

Member

Registered: 2007-06-10

Posts: 1

Isosceles Triangle

Problem:
I am observing an Isosceles Triangle with a Vertex Angle of "B" that is half of the base angle "A".

Question: What are "A" and "B" exactly?

I have an illustration which I copied down from the board, but the triangle has no specific angles or degrees, just a "B" on the top corner, and two "A's" on the bottom two corners of a rather typical looking triangle.  Is it a trick question from my math instructor?  My gut feel is to say that "A(2)" and "B" are 180 degrees exactly.  I am unsure.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Isosceles Triangle

Well, since it is an isosceles triangle, the two base angles must be equal, and all the angles add up to 180 degrees:

B + 2A = 180         ...[1]

You are given that:

B = 0.5A                ...[2]

Now that you have this pair of simultaneous equations, you can substitute [2] into [1] to solve for A

0.5A + 2A = 180
2.5A = 180
A = 72

Then, substitute A = 72 into [2]:

B = 0.5(72)
B = 36

Hence, angle A is 72 degrees, and angle B is 36 degrees. You can check these answers against the question instructions to make sure they match.