SOLUTION: one angle of a triangle is four times as large as another the measure of the third angle is 15 degrees more thatn that of the smallest angle find the measure of each angle

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Question 836951: one angle of a triangle is four times as large as another the measure of the third angle is 15 degrees more thatn that of the smallest angle find the measure of each angle
Answer by dfrazzetto(283)   (Show Source): You can put this solution on YOUR website!
Set angles a, b, c
Since all angles must be >0; assume b is smallest angle
a = 4b
a + b + c = 180
c = b + 15
a + b + c = 180; rewrite in terms of only angle 'b'
4b + b + b + 15 = 180
6b + 15 = 180
b = 27.5 degrees
a = 4b = 4(27.5) = 110 degrees
c = b + 15 = 27.5 + 15 = 42.5
CHECK:
27.5 + 110 + 42.5 = 180; Correct


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  • This is an equation! Solutions: b=27.5.
  • Graphical form: Equation was fully solved.
  • Text form: 4b+b+b+15=180 simplifies to 0=0
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DETAILED EXPLANATION

Look at .
Eliminated similar terms highlight_red%28+4%2Ab+%29,highlight_red%28+b+%29,highlight_red%28+b+%29 replacing them with highlight_green%28+%284%2B1%2B1%29%2Ab+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-180+%29
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Removed extra sign in front of -165
It becomes .
Look at .
Solved linear equation highlight_red%28+6%2Ab-165=0+%29 equivalent to 6*b-165 =0
It becomes .
Result:
This is an equation! Solutions: b=27.5.

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