SOLUTION: The second angle of a triangle is 4 times as large as the first. The third angle is 120° more than the sum of the other two angles. Find the measure of the second angle.

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Question 221519: The second angle of a triangle is 4 times as large as the first. The third angle is 120° more
than the sum of the other two angles. Find the measure of the second angle.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The second angle of a triangle is 4 times as large as the first. The third angle is 120° more than the sum of the other two angles. Find the measure of the second angle.

Step 1. Three angles of a triangle add up to 180 degrees.

Step 2. Let x be the first angle.

Step 3. Let 4x be the second angle since it's 4 times as large as the first.

Step 4. Let x+4x=5x be the sum of the first and second angles.

Step 5. Let 5x+120 be the third angle since it's 120 degrees more than the sum of the other two angles.

Step 6. Then, x+4x+5x+120=180 since the three angles add up to 180

Step 7. Solving the equation in Step 6 yields the following steps

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


YOUR ANSWER


  • This is an equation! Solutions: x=6.
  • Graphical form: Equation x%2B4x%2B5x%2B120=180 was fully solved.
  • Text form: x+4x+5x+120=180 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x%2B4x%2B5x%2B120=180+%29
    For tutors: simplify_cartoon( x+4x+5x+120=180 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+x+%29%2Bhighlight_red%28+4%2Ax+%29%2Bhighlight_red%28+5%2Ax+%29%2B120=180.
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+4%2Ax+%29,highlight_red%28+5%2Ax+%29 replacing them with highlight_green%28+%281%2B4%2B5%29%2Ax+%29
It becomes highlight_green%28+%281%2B4%2B5%29%2Ax+%29%2B120=180.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+4+%29%2Bhighlight_red%28+5+%29%29%2Ax%2B120=180.
Added fractions or integers together
It becomes %28highlight_green%28+10+%29%29%2Ax%2B120=180.
Look at highlight_red%28+%28highlight_red%28+10+%29%29%2Ax+%29%2B120=180.
Remove unneeded parentheses around factor highlight_red%28+10+%29
It becomes highlight_green%28+10+%29%2Ax%2B120=180.
Look at 10%2Ax%2B120=highlight_red%28+180+%29.
Moved these terms to the left highlight_green%28+-180+%29
It becomes 10%2Ax%2B120-highlight_green%28+180+%29=0.
Look at 10%2Ax%2Bhighlight_red%28+120+%29-highlight_red%28+180+%29=0.
Added fractions or integers together
It becomes 10%2Ax%2Bhighlight_green%28+-60+%29=0.
Look at 10%2Ax%2Bhighlight_red%28+-60+%29=0.
Removed extra sign in front of -60
It becomes 10%2Ax-highlight_green%28+60+%29=0.
Look at highlight_red%28+10%2Ax-60+%29=0.
Solved linear equation highlight_red%28+10%2Ax-60=0+%29 equivalent to 10*x-60 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=6.

Universal Simplifier and Solver


Done!



With x=6, then 4x=24 and 5x+120=150. Note these angles add up to 180 degrees.

Step 8. ANSWER: The three angles are 6 degrees, 24 degrees and 150 degrees.

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