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?
Found 2 solutions by Theo, ikleyn:
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.
Answer by ikleyn(52863)  (Show Source):
You can put this solution on YOUR website! .
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?
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The formulation of this problem is below floor level, i.e. is completely absurdist.
There is no such an isosceles right triangle with one of its base angle measure of 60 degrees.
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Simply the composer, who creates such problems,
is TOTALLY and FATALLY illiterate and incompetent in Math.
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As tutor @Theo solves this problem, leaving without his comments or corrections
the fact that the problem's formulation is incorrect, forces me to assume
that @Theo either did not read the problem or did not understand what was written in the post.
In this form, the problem is so  , that its only place is in a garbage bin.
Serious  to the creator of this problem for his or her complete incompetence in Math.
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