SOLUTION: Triangles ABC and RST are similar triangles. angle A= 2(x+15) angle S= 3x^0 and angle C= x^0. What measures of angles B,R,and T? What kind of triangles are they?

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Question 346968: Triangles ABC and RST are similar triangles. angle A= 2(x+15)
angle S= 3x^0 and
angle C= x^0. What measures of angles B,R,and T? What kind of triangles are they?

Answer by jsmallt9(3759) (Show Source):
You can put this solution on YOUR website!
First let's look at what you are given.

Since these two angles are:

You are also told that triangles ABC and RST are similar. In similar triangles all three pairs of corresponding angles are congruent. And the order of the letters in the names of the two triangles tell you which angles are corresponding: The first letters are A and R. So angle A and angle R correspond to each other and are, therefore, congruent. So if A = 2(x+15) then R = 2(x+15).

The second letters are B and S. So angle B and angle S correspond and are, therefore, congruent. So if S = 3 then B = 3. The third letters are C and T. So if C = 1 then T = 1.

With B = 3 and C = 1 then A must be 176 (since the three angles must add up to 180). This makes R = 176, too.

Equilateral triangles have 3 congruent angles and Isosceles triangle have two congruent angles. Triangles ABC and RST, with angles of 176, 3 and 1, have no congruent angles. So they are neither equilateral nor isosceles. They are scalene.