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?
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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
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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(b=75)}}}degrees
:
{{{highlight(a=b=75)}}}degrees
:
{{{highlight(c=(2/5)b=(2/5)75=30)}}}degrees