SOLUTION: find the measure of an angle if its measure is 3 degrees less than twice the measure of its complement.

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Question 215297: find the measure of an angle if its measure is 3 degrees less than twice the measure of its complement.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Find the measure of an angle if its measure is 3 degrees less than twice the measure of its complement.

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

Step 2. Let x be the angle and 90-x be its complementary angle

Step 3. Let 2(90-x) be twice the complementary angle

Step 4. Since the angle x is 3 degrees less than twice the measure of its complement, then x=2%2890-x%29-3.

Step 5. Solving the equation in Step 4 yields the following steps.

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


YOUR ANSWER


  • This is an equation! Solutions: x=59.
  • Graphical form: Equation x=2%2A%2890-x%29-3 was fully solved.
  • Text form: x=2*(90-x)-3 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x=2%2A%2890-x%29-3+%29
    For tutors: simplify_cartoon( x=2*(90-x)-3 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x=2%2A%28highlight_red%28+90+%29-x%29-3.
Moved 90 to the right of expression
It becomes x=2%2A%28-x%2Bhighlight_green%28+90+%29%29-3.
Look at x=highlight_red%28+2%2A%28-x%2B90%29-3+%29.
Moved these terms to the left highlight_green%28+-2%2A%28-x%2B90%29+%29,highlight_green%28+3+%29
It becomes x-highlight_green%28+2%2A%28-x%2B90%29+%29%2Bhighlight_green%28+3+%29=0.
Look at x-highlight_red%28+2%2A%28-x%2B90%29+%29%2B3=0.
Expanded term -2 by using associative property on %28-x%2B90%29
It becomes x%2Bhighlight_green%28+2%2Ax+%29-highlight_green%28+2%2A90+%29%2B3=0.
Look at x%2B2%2Ax-highlight_red%28+2+%29%2Ahighlight_red%28+90+%29%2B3=0.
Multiplied numerator integers
It becomes x%2B2%2Ax-highlight_green%28+180+%29%2B3=0.
Look at x%2B2%2Ax-highlight_red%28+180+%29%2Bhighlight_red%28+3+%29=0.
Added fractions or integers together
It becomes x%2B2%2Ax%2Bhighlight_green%28+-177+%29=0.
Look at x%2B2%2Ax%2Bhighlight_red%28+-177+%29=0.
Removed extra sign in front of -177
It becomes x%2B2%2Ax-highlight_green%28+177+%29=0.
Look at highlight_red%28+x+%29%2Bhighlight_red%28+2%2Ax+%29-177=0.
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+2%2Ax+%29 replacing them with highlight_green%28+%281%2B2%29%2Ax+%29
It becomes highlight_green%28+%281%2B2%29%2Ax+%29-177=0.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+2+%29%29%2Ax-177=0.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2Ax-177=0.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2Ax+%29-177=0.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2Ax-177=0.
Look at highlight_red%28+3%2Ax-177+%29=0.
Solved linear equation highlight_red%28+3%2Ax-177=0+%29 equivalent to 3*x-177 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=59.

Universal Simplifier and Solver


Done!



Step 6. ANSWER: The angle is 59 degrees

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J