SOLUTION: Twice the measure of the supplement of an angle is 39 degrees less than five times the complement of the angle. What is the measure of the angle? (Hint: Let 180 – x represent t

Algebra ->  Angles -> SOLUTION: Twice the measure of the supplement of an angle is 39 degrees less than five times the complement of the angle. What is the measure of the angle? (Hint: Let 180 – x represent t      Log On


   

Question 216674: Twice the measure of the supplement of an angle is 39 degrees less than five times the complement of the angle. What is the measure of the angle?
(Hint: Let 180 – x represent the supplement and 90 – x represent the complement.)
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Twice the measure of the supplement of an angle is 39 degrees less than five times the complement of the angle. What is the measure of the angle?
(Hint: Let 180 – x represent the supplement and 90 – x represent the complement.)

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 the supplement

Step 5. Let 90-x be the complement.

Step 6. Let 5*(90-x) be five times the complement and let 2(180-x) be twice the supplement.

Step 7. Then, 2(180-x) = 5(90-x) - 39 since twice the measure of the supplement of an angle is 39 degrees less than five times the complement of the angle. What is the measure of the angle?

Step 8. The following steps will solve the equation in Step 7.

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


YOUR ANSWER


  • This is an equation! Solutions: x=17.
  • Graphical form: Equation 2%2A%28180-x%29=5%2A%2890-x%29-39 was fully solved.
  • Text form: 2*(180-x)=5*(90-x)-39 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2%2A%28180-x%29=5%2A%2890-x%29-39+%29
    For tutors: simplify_cartoon( 2*(180-x)=5*(90-x)-39 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2A%28highlight_red%28+180+%29-x%29=5%2A%2890-x%29-39.
Moved 180 to the right of expression
It becomes 2%2A%28-x%2Bhighlight_green%28+180+%29%29=5%2A%2890-x%29-39.
Look at 2%2A%28-x%2B180%29=5%2A%28highlight_red%28+90+%29-x%29-39.
Moved 90 to the right of expression
It becomes 2%2A%28-x%2B180%29=5%2A%28-x%2Bhighlight_green%28+90+%29%29-39.
Look at 2%2A%28-x%2B180%29=highlight_red%28+5%2A%28-x%2B90%29-39+%29.
Moved these terms to the left highlight_green%28+-5%2A%28-x%2B90%29+%29,highlight_green%28+39+%29
It becomes 2%2A%28-x%2B180%29-highlight_green%28+5%2A%28-x%2B90%29+%29%2Bhighlight_green%28+39+%29=0.
Look at highlight_red%28+2%2A%28-x%2B180%29+%29-5%2A%28-x%2B90%29%2B39=0.
Expanded term 2 by using associative property on %28-x%2B180%29
It becomes -highlight_green%28+2%2Ax+%29%2Bhighlight_green%28+2%2A180+%29-5%2A%28-x%2B90%29%2B39=0.
Look at -2%2Ax%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+180+%29-5%2A%28-x%2B90%29%2B39=0.
Multiplied numerator integers
It becomes -2%2Ax%2Bhighlight_green%28+360+%29-5%2A%28-x%2B90%29%2B39=0.
Look at -2%2Ax%2Bhighlight_red%28+360+%29-5%2A%28-x%2B90%29%2Bhighlight_red%28+39+%29=0.
Added fractions or integers together
It becomes -2%2Ax%2Bhighlight_green%28+399+%29-5%2A%28-x%2B90%29=0.
Look at -2%2Ax%2Bhighlight_red%28+399+%29-5%2A%28-x%2B90%29=0.
Moved 399 to the right of expression
It becomes -2%2Ax-5%2A%28-x%2B90%29%2Bhighlight_green%28+399+%29=0.
Look at -2%2Ax-highlight_red%28+5%2A%28-x%2B90%29+%29%2B399=0.
Expanded term -5 by using associative property on %28-x%2B90%29
It becomes -2%2Ax%2Bhighlight_green%28+5%2Ax+%29-highlight_green%28+5%2A90+%29%2B399=0.
Look at -2%2Ax%2B5%2Ax-highlight_red%28+5+%29%2Ahighlight_red%28+90+%29%2B399=0.
Multiplied numerator integers
It becomes -2%2Ax%2B5%2Ax-highlight_green%28+450+%29%2B399=0.
Look at -2%2Ax%2B5%2Ax-highlight_red%28+450+%29%2Bhighlight_red%28+399+%29=0.
Added fractions or integers together
It becomes -2%2Ax%2B5%2Ax%2Bhighlight_green%28+-51+%29=0.
Look at -2%2Ax%2B5%2Ax%2Bhighlight_red%28+-51+%29=0.
Removed extra sign in front of -51
It becomes -2%2Ax%2B5%2Ax-highlight_green%28+51+%29=0.
Look at -highlight_red%28+2%2Ax+%29%2Bhighlight_red%28+5%2Ax+%29-51=0.
Eliminated similar terms highlight_red%28+-2%2Ax+%29,highlight_red%28+5%2Ax+%29 replacing them with highlight_green%28+%28-2%2B5%29%2Ax+%29
It becomes highlight_green%28+%28-2%2B5%29%2Ax+%29-51=0.
Look at %28-highlight_red%28+2+%29%2Bhighlight_red%28+5+%29%29%2Ax-51=0.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2Ax-51=0.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2Ax+%29-51=0.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2Ax-51=0.
Look at highlight_red%28+3%2Ax-51+%29=0.
Solved linear equation highlight_red%28+3%2Ax-51=0+%29 equivalent to 3*x-51 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=17.

Universal Simplifier and Solver


Done!



With x=17, then 180-x=163 and 90-x=73.

Check...2(180-x) = 5(90-x) - 39...2*163=5*73-39...which is a true statement.

Step 9. ANSWER: The angle is 17 degrees, its supplement is 163 degrees and its complement is 73 degrees.

I hope the above steps were helpful.

For FREE Step-By-Step videos in Introduction to Algebra, please visit
http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit
http://www.FreedomUniversity.TV/courses/Trigonometry.

Good luck in your studies!

Respectfully,
Dr J