SOLUTION: Each of the equal angles of an isosceles triangle measures 25 degree less than twice the vertex angle. Find the measure of the vertex angle.

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Question 126611: Each of the equal angles of an isosceles triangle measures 25 degree less than twice the vertex angle. Find the measure of the vertex angle.
Answer by solver91311(24713) About Me  (Show Source):
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If the vertex angle is x, then the equal angles must be 2x - 25. The sum of the interior angles of any triangle is 180 degrees, so:

%282x-25%29%2B%282x-25%29%2Bx=180

Collect terms:
5x-50=180
5x=230
x=46

So, the vertex angle is 46. Twice the vertex angle is 92. 25 less than that is 67, so the equal angles measure 67.

Check:
46 + 67 + 67 = 180. Check.