SOLUTION: The measure of each base angle of an isosceles triangle is 10 degrees less than twice the measure of the vertex angle. Find the measure of each angle of the triangle.

Algebra ->  Triangles -> SOLUTION: The measure of each base angle of an isosceles triangle is 10 degrees less than twice the measure of the vertex angle. Find the measure of each angle of the triangle.       Log On


   

Question 223445: The measure of each base angle of an isosceles triangle is 10 degrees less than twice the measure of the vertex angle. Find the measure of each angle of the triangle.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the vertex angle be x degrees, then each base angle is 2x-10, and the sum of these three angles is 180 degrees, so...
(2x-10)+(2x-10)+x = 180 Combine the like-terms.
5x-20 = 180 Add 20 to bothe sides.
5x = 200 Divide both sides by 5.
x = 40 degrees.
2x-10 = 70 degrees.
The three angles are:
Vertex angle = 40 degrees.
The base angles are each 70 degrees.