SOLUTION: can you please help me figure out the supplement of a given angle is four times as large as a complement of the angle. Find the measure of the given angle. Please.

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Question 224936: can you please help me figure out the supplement of a given angle is four times as large as a complement of the angle. Find the measure of the given angle. Please.
Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
Can you please help me figure out the supplement of a given angle is four times as large as a complement of the angle. Find the measure of the given angle. Please.

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. Then 180-x=4(90-x) since the supplement of a given angle is four times as large as a complement of the angle

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


YOUR ANSWER


  • This is an equation! Solutions: x=60.
  • Graphical form: Equation was fully solved.
  • Text form: 180-x=4*(90-x) simplifies to 0=0
  • Cartoon (animation) form:
    For tutors: simplify_cartoon( 180-x=4*(90-x) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Moved 180 to the right of expression
It becomes .
Look at .
Moved 90 to the right of expression
It becomes .
Look at .
Moved these terms to the left highlight_green%28+-4%2A%28-x%2B90%29+%29
It becomes .
Look at .
Moved 180 to the right of expression
It becomes .
Look at .
Expanded term -4 by using associative property on %28-x%2B90%29
It becomes .
Look at .
Multiplied numerator integers
It becomes .
Look at .
Added fractions or integers together
It becomes .
Look at .
Removed extra sign in front of -180
It becomes .
Look at .
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 .
Look at .
Added fractions or integers together
It becomes .
Look at .
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes .
Look at .
Solved linear equation highlight_red%28+3%2Ax-180=0+%29 equivalent to 3*x-180 =0
It becomes .
Result:
This is an equation! Solutions: x=60.

Universal Simplifier and Solver


Done!



With x=60, then 180-x-120 and 90-60=30 and note that four times the complement of the angle is the supplement of the angle.

Step 7. ANSWER: The angle is 60 degrees. It complement is 30 degrees and its supplement is 120 degrees.

I hope the above steps were helpful.

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And good luck in your studies!

Respectfully,
Dr J
drjctu@gmail.com
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