SOLUTION: three times the measure of the angle is twice that of its complement

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Question 218679: three times the measure of the angle is twice that of its complement
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Three times the measure of the angle is twice that of its complement.

Step 1. Complementary angles means that two angles add up to 90 degrees.

Step 2. Let x be the angle and 3x be three times the angle.

Step 3. Let 90-x be its complement and 2(90-x) be twice its complement.

Step 4. Then 3x=2(90-x) since three time the measure of the angle is twice that of its complement.

Step 5. Solving yields the following steps:

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


YOUR ANSWER


  • This is an equation! Solutions: x=36.
  • Graphical form: Equation 3x=2%2A%2890-x%29 was fully solved.
  • Text form: 3x=2*(90-x) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+3x=2%2A%2890-x%29+%29
    For tutors: simplify_cartoon( 3x=2*(90-x) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 3%2Ax=2%2A%28highlight_red%28+90+%29-x%29.
Moved 90 to the right of expression
It becomes 3%2Ax=2%2A%28-x%2Bhighlight_green%28+90+%29%29.
Look at 3%2Ax=highlight_red%28+2%2A%28-x%2B90%29+%29.
Moved these terms to the left highlight_green%28+-2%2A%28-x%2B90%29+%29
It becomes 3%2Ax-highlight_green%28+2%2A%28-x%2B90%29+%29=0.
Look at 3%2Ax-highlight_red%28+2%2A%28-x%2B90%29+%29=0.
Expanded term -2 by using associative property on %28-x%2B90%29
It becomes 3%2Ax%2Bhighlight_green%28+2%2Ax+%29-highlight_green%28+2%2A90+%29=0.
Look at 3%2Ax%2B2%2Ax-highlight_red%28+2+%29%2Ahighlight_red%28+90+%29=0.
Multiplied numerator integers
It becomes 3%2Ax%2B2%2Ax-highlight_green%28+180+%29=0.
Look at highlight_red%28+3%2Ax+%29%2Bhighlight_red%28+2%2Ax+%29-180=0.
Eliminated similar terms highlight_red%28+3%2Ax+%29,highlight_red%28+2%2Ax+%29 replacing them with highlight_green%28+%283%2B2%29%2Ax+%29
It becomes highlight_green%28+%283%2B2%29%2Ax+%29-180=0.
Look at %28highlight_red%28+3+%29%2Bhighlight_red%28+2+%29%29%2Ax-180=0.
Added fractions or integers together
It becomes %28highlight_green%28+5+%29%29%2Ax-180=0.
Look at highlight_red%28+%28highlight_red%28+5+%29%29%2Ax+%29-180=0.
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes highlight_green%28+5+%29%2Ax-180=0.
Look at highlight_red%28+5%2Ax-180+%29=0.
Solved linear equation highlight_red%28+5%2Ax-180=0+%29 equivalent to 5*x-180 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=36.

Universal Simplifier and Solver


Done!



Then x=36 and 90-x=54

Check 3x=2(90-x) or 3*36=2*54...which is a true statement.

Step 6. ANSWER: The angles are 36 and 54 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.

And good luck in your studies!

Respectfully,
Dr J
http://www.FreedomUniversity.TV