SOLUTION: The measure of the supplement of an angle exceeds twice the measure of the complement of the angle by 20. Find the measure of half of the complement.

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Question 214862This question is from textbook
: The measure of the supplement of an angle exceeds twice the measure of the complement of the angle by 20. Find the measure of half of the complement. This question is from textbook

Answer by drj(1380) About Me  (Show Source):
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The measure of the supplement of an angle exceeds twice the measure of the complement of the angle by 20. Find the measure of half of the complement.

Step 1. The supplement is when two angles add up to 180 degrees.

Step 2. The complement is when two angles add up to 90 degrees.

Step 3. Let x be the angle, let 180-x be it supplement, let 90-x be its complement.

Step 4. Let 2(90-x) be twice the complement of the angle.

Step 5. 180=2(90-x)+20 The measure of the supplement of an angle exceeds twice the measure of the complement of the angle by 20

Step 6. The following will solve for the angle x in Step 5.

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


YOUR ANSWER


  • This is an equation! Solutions: x=10.
  • Graphical form: Equation 180=2%2A%2890-x%29%2B20 was fully solved.
  • Text form: 180=2*(90-x)+20 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+180=2%2A%2890-x%29%2B20+%29
    For tutors: simplify_cartoon( 180=2*(90-x)+20 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 180=2%2A%28highlight_red%28+90+%29-x%29%2B20.
Moved 90 to the right of expression
It becomes 180=2%2A%28-x%2Bhighlight_green%28+90+%29%29%2B20.
Look at 180=highlight_red%28+2%2A%28-x%2B90%29%2B20+%29.
Moved these terms to the left highlight_green%28+-2%2A%28-x%2B90%29+%29,highlight_green%28+-20+%29
It becomes 180-highlight_green%28+2%2A%28-x%2B90%29+%29-highlight_green%28+20+%29=0.
Look at highlight_red%28+180+%29-2%2A%28-x%2B90%29-highlight_red%28+20+%29=0.
Added fractions or integers together
It becomes highlight_green%28+160+%29-2%2A%28-x%2B90%29=0.
Look at highlight_red%28+160+%29-2%2A%28-x%2B90%29=0.
Moved 160 to the right of expression
It becomes -2%2A%28-x%2B90%29%2Bhighlight_green%28+160+%29=0.
Look at -highlight_red%28+2%2A%28-x%2B90%29+%29%2B160=0.
Expanded term -2 by using associative property on %28-x%2B90%29
It becomes highlight_green%28+2%2Ax+%29-highlight_green%28+2%2A90+%29%2B160=0.
Look at 2%2Ax-highlight_red%28+2+%29%2Ahighlight_red%28+90+%29%2B160=0.
Multiplied numerator integers
It becomes 2%2Ax-highlight_green%28+180+%29%2B160=0.
Look at 2%2Ax-highlight_red%28+180+%29%2Bhighlight_red%28+160+%29=0.
Added fractions or integers together
It becomes 2%2Ax%2Bhighlight_green%28+-20+%29=0.
Look at 2%2Ax%2Bhighlight_red%28+-20+%29=0.
Removed extra sign in front of -20
It becomes 2%2Ax-highlight_green%28+20+%29=0.
Look at highlight_red%28+2%2Ax-20+%29=0.
Solved linear equation highlight_red%28+2%2Ax-20=0+%29 equivalent to 2*x-20 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=10.

Universal Simplifier and Solver


Done!



When x=10, then the complement 90-x=80 and one-half the complement is 80/2=40.

Step 7. ANSWER. One-half the complement is 40 degrees.

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J