SOLUTION: What is the measure of an angle if twice the measure of its supplement is 30 more than 5 times the measure of it's comlement ?

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Question 214086: What is the measure of an angle if twice the measure of its supplement is 30 more than 5 times the measure of it's comlement ?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
What is the measure of an angle if twice the measure of its supplement is 30 more than 5 times the measure of its complement ?

Step 1. Supplementary angles is when two angles add up to 180 degrees and complementary angles is when two angles add up to 90 degrees.

Step 2. Let x be the angle, let 90-x be its complement and 180-x be its supplement.

Step 3. 2(180-x) twice the measure of its supplement.

Step 4. 5(90-x) five times the measure of its complement

Step 5. 2(180-x)=5(90-x)+30 Measure of an angle if twice the measure of its supplement is 30 more than 5 times the measure of its complement

Step 6. The following will solve the equation in Step 5.

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


YOUR ANSWER


  • This is an equation! Solutions: x=40.
  • Graphical form: Equation 2%2A%28180-x%29=5%2A%2890-x%29%2B30 was fully solved.
  • Text form: 2*(180-x)=5*(90-x)+30 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2%2A%28180-x%29=5%2A%2890-x%29%2B30+%29
    For tutors: simplify_cartoon( 2*(180-x)=5*(90-x)+30 )
  • 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%2B30.
Moved 180 to the right of expression
It becomes 2%2A%28-x%2Bhighlight_green%28+180+%29%29=5%2A%2890-x%29%2B30.
Look at 2%2A%28-x%2B180%29=5%2A%28highlight_red%28+90+%29-x%29%2B30.
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%2B30.
Look at 2%2A%28-x%2B180%29=highlight_red%28+5%2A%28-x%2B90%29%2B30+%29.
Moved these terms to the left highlight_green%28+-5%2A%28-x%2B90%29+%29,highlight_green%28+-30+%29
It becomes 2%2A%28-x%2B180%29-highlight_green%28+5%2A%28-x%2B90%29+%29-highlight_green%28+30+%29=0.
Look at highlight_red%28+2%2A%28-x%2B180%29+%29-5%2A%28-x%2B90%29-30=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%29-30=0.
Look at -2%2Ax%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+180+%29-5%2A%28-x%2B90%29-30=0.
Multiplied numerator integers
It becomes -2%2Ax%2Bhighlight_green%28+360+%29-5%2A%28-x%2B90%29-30=0.
Look at -2%2Ax%2Bhighlight_red%28+360+%29-5%2A%28-x%2B90%29-highlight_red%28+30+%29=0.
Added fractions or integers together
It becomes -2%2Ax%2Bhighlight_green%28+330+%29-5%2A%28-x%2B90%29=0.
Look at -2%2Ax%2Bhighlight_red%28+330+%29-5%2A%28-x%2B90%29=0.
Moved 330 to the right of expression
It becomes -2%2Ax-5%2A%28-x%2B90%29%2Bhighlight_green%28+330+%29=0.
Look at -2%2Ax-highlight_red%28+5%2A%28-x%2B90%29+%29%2B330=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%2B330=0.
Look at -2%2Ax%2B5%2Ax-highlight_red%28+5+%29%2Ahighlight_red%28+90+%29%2B330=0.
Multiplied numerator integers
It becomes -2%2Ax%2B5%2Ax-highlight_green%28+450+%29%2B330=0.
Look at -2%2Ax%2B5%2Ax-highlight_red%28+450+%29%2Bhighlight_red%28+330+%29=0.
Added fractions or integers together
It becomes -2%2Ax%2B5%2Ax%2Bhighlight_green%28+-120+%29=0.
Look at -2%2Ax%2B5%2Ax%2Bhighlight_red%28+-120+%29=0.
Removed extra sign in front of -120
It becomes -2%2Ax%2B5%2Ax-highlight_green%28+120+%29=0.
Look at -highlight_red%28+2%2Ax+%29%2Bhighlight_red%28+5%2Ax+%29-120=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+%29-120=0.
Look at %28-highlight_red%28+2+%29%2Bhighlight_red%28+5+%29%29%2Ax-120=0.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2Ax-120=0.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2Ax+%29-120=0.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2Ax-120=0.
Look at highlight_red%28+3%2Ax-120+%29=0.
Solved linear equation highlight_red%28+3%2Ax-120=0+%29 equivalent to 3*x-120 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=40.

Universal Simplifier and Solver


Done!




Step 7. The complement of the angle x=40 is 90-x=50.

Step 8. ANSWER. The complement of the angle is 50 degree

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