SOLUTION: Two angles in a triangle are equal and their sum is five times the third angle in the triangle. What are the measures of each of the three interior angles?

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Question 181671: Two angles in a triangle are equal and their sum is five times the third angle in the triangle. What are the measures of each of the three interior angles?
Answer by Mathtut(3670) About Me  (Show Source):
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Two angles in a triangle are equal and their sum is five times the third angle in the triangle. What are the measures of each of the three interior angles?
:
let a, b and c be our angles
:
a=b.........eq 1
a+b=5c......eq 2
a+b+c=180...eq 3
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take a's value from eq 1 and plug it into eq 2.---->b+b=5c-->2b=5c-->c=(2/5)b
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now take a's value from eq 1 and our new found value of c which is (2/5)b and plug those into eq 3
:
b+b+(2/5)b=180
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5b+5b+2b=900.........multiplied all terms by 5 to eliminate the fraction
:
12b=900
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highlight%28b=75%29degrees
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highlight%28a=b=75%29degrees
:
highlight%28c=%282%2F5%29b=%282%2F5%2975=30%29degrees