SOLUTION: what is the measure if the vertex angle of an isosceles right triangle when one of its base angles has a measure of 60 degree?

Question 480043: what is the measure if the vertex angle of an isosceles right triangle when one of its base angles has a measure of 60 degree?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the base angles of an isosceles triangle are equal so the sum of the 2 base angles is equal to 120 degrees.
the sum of all 3 angles of a triangle is 180 degrees, so the third angle is 180 - 120 = 60 degrees.
in this case your isosceles triangle becomes an equilateral triangle.
all 3 sides are equal.
all 3 angles are equal.
because 2 sides and 2 angles are equal, it is an isosceles triangle.
because 3 sides and 3 angles are equal, it is an equilateral triangle.
the answer to your question, however, is simply that the vertex angle is 60 degrees if one of the base angles is 60 degrees for the reasons outlined above.

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