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) About Me  (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


Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: b=27.5.
  • Graphical form: Equation 4b%2Bb%2Bb%2B15=180 was fully solved.
  • Text form: 4b+b+b+15=180 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+4b%2Bb%2Bb%2B15=180+%29
    For tutors: simplify_cartoon( 4b+b+b+15=180 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+4%2Ab+%29%2Bhighlight_red%28+b+%29%2Bhighlight_red%28+b+%29%2B15=180.
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 highlight_green%28+%284%2B1%2B1%29%2Ab+%29%2B15=180.
Look at %28highlight_red%28+4+%29%2Bhighlight_red%28+1+%29%2Bhighlight_red%28+1+%29%29%2Ab%2B15=180.
Added fractions or integers together
It becomes %28highlight_green%28+6+%29%29%2Ab%2B15=180.
Look at highlight_red%28+%28highlight_red%28+6+%29%29%2Ab+%29%2B15=180.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes highlight_green%28+6+%29%2Ab%2B15=180.
Look at 6%2Ab%2B15=highlight_red%28+180+%29.
Moved these terms to the left highlight_green%28+-180+%29
It becomes 6%2Ab%2B15-highlight_green%28+180+%29=0.
Look at 6%2Ab%2Bhighlight_red%28+15+%29-highlight_red%28+180+%29=0.
Added fractions or integers together
It becomes 6%2Ab%2Bhighlight_green%28+-165+%29=0.
Look at 6%2Ab%2Bhighlight_red%28+-165+%29=0.
Removed extra sign in front of -165
It becomes 6%2Ab-highlight_green%28+165+%29=0.
Look at highlight_red%28+6%2Ab-165+%29=0.
Solved linear equation highlight_red%28+6%2Ab-165=0+%29 equivalent to 6*b-165 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: b=27.5.

Universal Simplifier and Solver


Done!