SOLUTION: The vertex angle of an isosceles triangle is 64 degrees. find the measure of a base angle

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Question 118610: The vertex angle of an isosceles triangle is 64 degrees. find the measure of a base angle
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Remember, in any triangle, the sum of all three angles is 180 degrees. Also, if angle x is the vertex angle and angles y and z are the base angles (these angles are equal ie y=z),

So the sum of the three angles is represented by this equation:
x%2By%2Bz=180

x%2Bz%2Bz=180 Now plug in y=z


x%2B2z=180 Combine like terms

Since we know that the vertex angle of the isosceles triangle is 64 degrees, this means x=64

64%2B2z=180 Now plug in x=64 into the equation



2z=180-64Subtract 64 from both sides


2z=116 Combine like terms on the right side


z=%28116%29%2F%282%29 Divide both sides by 2 to isolate y



z=58 Divide


So the base angles are both 58 degrees