SOLUTION: The measure of the supplement of an angle is 30 less than four times the measure of the complement of the angle. Find the measure of the angle.

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Question 214288: The measure of the supplement of an angle is 30 less than four times the measure of the complement of the angle. Find the measure of the angle.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The measure of the supplement of an angle is 30 less than four times the measure of the complement of the angle. Find the measure of the angle.

Step 1. Let x be the measure of the angle.

Step 2. Supplement means two angles add up to 180 degrees and complement is when two angles add up to 90 degrees. These angles have a common side.

Step 3. 180-x is the supplement of the angle and 90-x is the complement of the angle.

Step 4. 180-x=4(90-x)+30 Supplement of an angle is 30 less than four times the measure of the complement of the angle. Find the measure of the angle.

Step 5. The following steps will solve 180-x=4(90-x)+30

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


YOUR ANSWER


  • This is an equation! Solutions: x=70.
  • Graphical form: Equation 180-x=4%2A%2890-x%29%2B30 was fully solved.
  • Text form: 180-x=4*(90-x)+30 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+180-x=4%2A%2890-x%29%2B30+%29
    For tutors: simplify_cartoon( 180-x=4*(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=4%2A%2890-x%29%2B30.
Moved 180 to the right of expression
It becomes -x%2Bhighlight_green%28+180+%29=4%2A%2890-x%29%2B30.
Look at -x%2B180=4%2A%28highlight_red%28+90+%29-x%29%2B30.
Moved 90 to the right of expression
It becomes -x%2B180=4%2A%28-x%2Bhighlight_green%28+90+%29%29%2B30.
Look at -x%2B180=highlight_red%28+4%2A%28-x%2B90%29%2B30+%29.
Moved these terms to the left highlight_green%28+-4%2A%28-x%2B90%29+%29,highlight_green%28+-30+%29
It becomes -x%2B180-highlight_green%28+4%2A%28-x%2B90%29+%29-highlight_green%28+30+%29=0.
Look at -x%2Bhighlight_red%28+180+%29-4%2A%28-x%2B90%29-highlight_red%28+30+%29=0.
Added fractions or integers together
It becomes -x%2Bhighlight_green%28+150+%29-4%2A%28-x%2B90%29=0.
Look at -x%2Bhighlight_red%28+150+%29-4%2A%28-x%2B90%29=0.
Moved 150 to the right of expression
It becomes -x-4%2A%28-x%2B90%29%2Bhighlight_green%28+150+%29=0.
Look at -x-highlight_red%28+4%2A%28-x%2B90%29+%29%2B150=0.
Expanded term -4 by using associative property on %28-x%2B90%29
It becomes -x%2Bhighlight_green%28+4%2Ax+%29-highlight_green%28+4%2A90+%29%2B150=0.
Look at -x%2B4%2Ax-highlight_red%28+4+%29%2Ahighlight_red%28+90+%29%2B150=0.
Multiplied numerator integers
It becomes -x%2B4%2Ax-highlight_green%28+360+%29%2B150=0.
Look at -x%2B4%2Ax-highlight_red%28+360+%29%2Bhighlight_red%28+150+%29=0.
Added fractions or integers together
It becomes -x%2B4%2Ax%2Bhighlight_green%28+-210+%29=0.
Look at -x%2B4%2Ax%2Bhighlight_red%28+-210+%29=0.
Removed extra sign in front of -210
It becomes -x%2B4%2Ax-highlight_green%28+210+%29=0.
Look at -highlight_red%28+x+%29%2Bhighlight_red%28+4%2Ax+%29-210=0.
Eliminated similar terms highlight_red%28+-x+%29,highlight_red%28+4%2Ax+%29 replacing them with highlight_green%28+%28-1%2B4%29%2Ax+%29
It becomes highlight_green%28+%28-1%2B4%29%2Ax+%29-210=0.
Look at %28-highlight_red%28+1+%29%2Bhighlight_red%28+4+%29%29%2Ax-210=0.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2Ax-210=0.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2Ax+%29-210=0.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2Ax-210=0.
Look at highlight_red%28+3%2Ax-210+%29=0.
Solved linear equation highlight_red%28+3%2Ax-210=0+%29 equivalent to 3*x-210 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=70.

Universal Simplifier and Solver


Done!



Step 6. The measure of the angle is 70 degrees.

Note that 180-70=4(90-70)+30 is a true statement.

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