SOLUTION: the measure of the supplement of an angle exceeds three times the measure of the compliment by 30.

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Question 221642: the measure of the supplement of an angle exceeds three times the measure of the compliment by 30.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The measure of the supplement of an angle exceeds three times the measure of the complement by 30.

Step 1. Supplementary angles means two angles add up to 180 degrees.

Step 2. Complementary angles means two angles add up to 90 degrees.

Step 3. Let x be the angle.

Step 4. Let 180-x be its supplementary angle.

Step 5. Let 90-x be its complementary angle.

Step 6. Let 3(90-x) be three times the complement.

Step 7. Then 180-x=3(90-x)+30 since the measure of the supplement of an angle exceeds three times the measure of the complement by 30.

Step 8. Solving the equation in Step 7 yields the following steps:

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


YOUR ANSWER


  • This is an equation! Solutions: x=60.
  • Graphical form: Equation 180-x=3%2A%2890-x%29%2B30 was fully solved.
  • Text form: 180-x=3*(90-x)+30 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+180-x=3%2A%2890-x%29%2B30+%29
    For tutors: simplify_cartoon( 180-x=3*(90-x)+30 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+180+%29-x=3%2A%2890-x%29%2B30.
Moved 180 to the right of expression
It becomes -x%2Bhighlight_green%28+180+%29=3%2A%2890-x%29%2B30.
Look at -x%2B180=3%2A%28highlight_red%28+90+%29-x%29%2B30.
Moved 90 to the right of expression
It becomes -x%2B180=3%2A%28-x%2Bhighlight_green%28+90+%29%29%2B30.
Look at -x%2B180=highlight_red%28+3%2A%28-x%2B90%29%2B30+%29.
Moved these terms to the left highlight_green%28+-3%2A%28-x%2B90%29+%29,highlight_green%28+-30+%29
It becomes -x%2B180-highlight_green%28+3%2A%28-x%2B90%29+%29-highlight_green%28+30+%29=0.
Look at -x%2Bhighlight_red%28+180+%29-3%2A%28-x%2B90%29-highlight_red%28+30+%29=0.
Added fractions or integers together
It becomes -x%2Bhighlight_green%28+150+%29-3%2A%28-x%2B90%29=0.
Look at -x%2Bhighlight_red%28+150+%29-3%2A%28-x%2B90%29=0.
Moved 150 to the right of expression
It becomes -x-3%2A%28-x%2B90%29%2Bhighlight_green%28+150+%29=0.
Look at -x-highlight_red%28+3%2A%28-x%2B90%29+%29%2B150=0.
Expanded term -3 by using associative property on %28-x%2B90%29
It becomes -x%2Bhighlight_green%28+3%2Ax+%29-highlight_green%28+3%2A90+%29%2B150=0.
Look at -x%2B3%2Ax-highlight_red%28+3+%29%2Ahighlight_red%28+90+%29%2B150=0.
Multiplied numerator integers
It becomes -x%2B3%2Ax-highlight_green%28+270+%29%2B150=0.
Look at -x%2B3%2Ax-highlight_red%28+270+%29%2Bhighlight_red%28+150+%29=0.
Added fractions or integers together
It becomes -x%2B3%2Ax%2Bhighlight_green%28+-120+%29=0.
Look at -x%2B3%2Ax%2Bhighlight_red%28+-120+%29=0.
Removed extra sign in front of -120
It becomes -x%2B3%2Ax-highlight_green%28+120+%29=0.
Look at -highlight_red%28+x+%29%2Bhighlight_red%28+3%2Ax+%29-120=0.
Eliminated similar terms highlight_red%28+-x+%29,highlight_red%28+3%2Ax+%29 replacing them with highlight_green%28+%28-1%2B3%29%2Ax+%29
It becomes highlight_green%28+%28-1%2B3%29%2Ax+%29-120=0.
Look at %28-highlight_red%28+1+%29%2Bhighlight_red%28+3+%29%29%2Ax-120=0.
Added fractions or integers together
It becomes %28highlight_green%28+2+%29%29%2Ax-120=0.
Look at highlight_red%28+%28highlight_red%28+2+%29%29%2Ax+%29-120=0.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes highlight_green%28+2+%29%2Ax-120=0.
Look at highlight_red%28+2%2Ax-120+%29=0.
Solved linear equation highlight_red%28+2%2Ax-120=0+%29 equivalent to 2*x-120 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=60.

Universal Simplifier and Solver


Done!



With x=60, then 180-x=120 and 90-x=30.

Check equation 180-x=3(90-x)+30 of Step 7 or 120=3*30+30=120 which is a true statement

Step 9. ANSWER: The angle is 60, its supplement is 120 and its complement is 30.


I hope the above steps were helpful.

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And good luck in your studies!

Respectfully,
Dr J
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