SOLUTION: Five times the measure of an angle less the complement of that angle equals 9. Find the measure of the angle.

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Question 215691: Five times the measure of an angle less the complement of that angle equals 9. Find the measure of the angle.
Found 2 solutions by drj, checkley77:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Five times the measure of an angle less the complement of that angle equals 9. Find the measure of the angle.

Step 1. Angles are complementary when the two angles add to 90 degrees.

Step 2. Let x be the angle and 90-x be the complementary angle.

Step 3. Let 5x be five times the angle.

Step 4. Then 5x-(90-x)=9 since five times the measure of an angle less the complement of that angle equals 9

Step 5. The following will solve the equation in Step 4:

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


YOUR ANSWER


  • This is an equation! Solutions: x=16.5.
  • Graphical form: Equation 5x-%2890-x%29=9 was fully solved.
  • Text form: 5x-(90-x)=9 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+5x-%2890-x%29=9+%29
    For tutors: simplify_cartoon( 5x-(90-x)=9 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 5%2Ax-highlight_red%28+%2890-x%29+%29=9.
Remove unneeded parentheses around terms highlight_red%28+-90+%29,highlight_red%28+x+%29
It becomes 5%2Ax-highlight_green%28+90+%29%2Bhighlight_green%28+x+%29=9.
Look at 5%2Ax-highlight_red%28+90+%29%2Bx=9.
Moved -90 to the right of expression
It becomes 5%2Ax%2Bx-highlight_green%28+90+%29=9.
Look at highlight_red%28+5%2Ax+%29%2Bhighlight_red%28+x+%29-90=9.
Eliminated similar terms highlight_red%28+5%2Ax+%29,highlight_red%28+x+%29 replacing them with highlight_green%28+%285%2B1%29%2Ax+%29
It becomes highlight_green%28+%285%2B1%29%2Ax+%29-90=9.
Look at %28highlight_red%28+5+%29%2Bhighlight_red%28+1+%29%29%2Ax-90=9.
Added fractions or integers together
It becomes %28highlight_green%28+6+%29%29%2Ax-90=9.
Look at highlight_red%28+%28highlight_red%28+6+%29%29%2Ax+%29-90=9.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes highlight_green%28+6+%29%2Ax-90=9.
Look at 6%2Ax-90=highlight_red%28+9+%29.
Moved these terms to the left highlight_green%28+-9+%29
It becomes 6%2Ax-90-highlight_green%28+9+%29=0.
Look at 6%2Ax-highlight_red%28+90+%29-highlight_red%28+9+%29=0.
Added fractions or integers together
It becomes 6%2Ax%2Bhighlight_green%28+-99+%29=0.
Look at 6%2Ax%2Bhighlight_red%28+-99+%29=0.
Removed extra sign in front of -99
It becomes 6%2Ax-highlight_green%28+99+%29=0.
Look at highlight_red%28+6%2Ax-99+%29=0.
Solved linear equation highlight_red%28+6%2Ax-99=0+%29 equivalent to 6*x-99 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=16.5.

Universal Simplifier and Solver


Done!




With x=16.5 , then 90-x=73.5

Check 5x-90-x=5*16.5-73.5=9 which is a true statement.

Step 6. The angle is 16.5 degrees and its complement is 73.5 degrees.

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
5x-(90-x)=9
5x-90+x=9
6x=9+90
6x=99
x=99/6
x=16.5 degrees.
Proof:
5*16.5-(90-16.5)=9
82.5-(90-16.5)=9
82.5-73.5=9
9=9