SOLUTION: Find the measures of the angles of an isosceles triangle if the measure of the vertex angle is 40 degrees less than the sum of the measures of the base angles

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Question 16275: Find the measures of the angles of an isosceles triangle if the measure of the vertex angle is 40 degrees less than the sum of the measures of the base angles
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
As you probably know, the base angles in an isosceles triangle are equal. Let's call one of these base angles x.
And you are also most likely aware that the sum of the interior angles of any plane triangle is 180 degrees. From the problem description, we can write: (2x - 40) is the vertex angle.
Putting it all together then, we can wite:
2x+%2B+%282x-40%29+=+180 Simplify and solve for x.
4x+-+40+=+180 Add 40 to both sides.
4x+=+220 Divide both sides by 4.
x+=+55
Each base angle is 55 degrees.
The vertex angle is: 2(55) - 40 = 110 - 40 = 70 degrees.
Check: 55 + 55 + 70 = 180