SOLUTION: if one-half of the complement of an angle plus three-fourths of the supplement of the angle equals 110, find the measure of the angle.

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Question 215331: if one-half of the complement of an angle plus three-fourths of the supplement of the angle equals 110, find the measure of the angle.
Found 2 solutions by drj, ankor@dixie-net.com:
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
If one-half of the complement of an angle plus three-fourths of the supplement of the angle equals 110. Find the measure of the angle.

Step 1. Let x be the angle.

Step 2. Complementary angles means two angles add up to 90 degrees and supplementary angles means two angles add up to 180 degrees.

Step 3. Let 90-x be the complementary angle of x and 180-x be the supplementary angle of x.

Step 4. Let %2890-x%29%2F2 be one half of the complementary angle.

Step 5. Let 3%28180-x%29%2F4 be 3/4 of the supplementary angle.

Step 6. Adding Steps 4 and 5 will be 110 degrees as given by the problem statement or in equation form we have

%2890-x%29%2F2%2B3%28180-x%29%2F4=110

Multiply by 4 to both sides of the equation toget rid of denominators

4%2A%2890-x%29%2F2%2B4%2A3%28180-x%29%2F4=4%2A110


2%2A%2890-x%29%2B3%28180-x%29=440

Step 7. Solving for x yields the following steps:

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


YOUR ANSWER


  • This is an equation! Solutions: x=56.
  • Graphical form: Equation 2%2A%2890-x%29%2B3%2A%28180-x%29=440 was fully solved.
  • Text form: 2*(90-x)+3*(180-x)=440 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+2%2A%2890-x%29%2B3%2A%28180-x%29=440+%29
    For tutors: simplify_cartoon( 2*(90-x)+3*(180-x)=440 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at 2%2A%28highlight_red%28+90+%29-x%29%2B3%2A%28180-x%29=440.
Moved 90 to the right of expression
It becomes 2%2A%28-x%2Bhighlight_green%28+90+%29%29%2B3%2A%28180-x%29=440.
Look at 2%2A%28-x%2B90%29%2B3%2A%28highlight_red%28+180+%29-x%29=440.
Moved 180 to the right of expression
It becomes 2%2A%28-x%2B90%29%2B3%2A%28-x%2Bhighlight_green%28+180+%29%29=440.
Look at 2%2A%28-x%2B90%29%2B3%2A%28-x%2B180%29=highlight_red%28+440+%29.
Moved these terms to the left highlight_green%28+-440+%29
It becomes 2%2A%28-x%2B90%29%2B3%2A%28-x%2B180%29-highlight_green%28+440+%29=0.
Look at highlight_red%28+2%2A%28-x%2B90%29+%29%2B3%2A%28-x%2B180%29-440=0.
Expanded term 2 by using associative property on %28-x%2B90%29
It becomes -highlight_green%28+2%2Ax+%29%2Bhighlight_green%28+2%2A90+%29%2B3%2A%28-x%2B180%29-440=0.
Look at -2%2Ax%2Bhighlight_red%28+2+%29%2Ahighlight_red%28+90+%29%2B3%2A%28-x%2B180%29-440=0.
Multiplied numerator integers
It becomes -2%2Ax%2Bhighlight_green%28+180+%29%2B3%2A%28-x%2B180%29-440=0.
Look at -2%2Ax%2Bhighlight_red%28+180+%29%2B3%2A%28-x%2B180%29-highlight_red%28+440+%29=0.
Added fractions or integers together
It becomes -2%2Ax%2Bhighlight_green%28+-260+%29%2B3%2A%28-x%2B180%29=0.
Look at -2%2Ax%2Bhighlight_red%28+-260+%29%2B3%2A%28-x%2B180%29=0.
Moved -260 to the right of expression
It becomes -2%2Ax%2B3%2A%28-x%2B180%29%2Bhighlight_green%28+-260+%29=0.
Look at -2%2Ax%2B3%2A%28-x%2B180%29%2Bhighlight_red%28+-260+%29=0.
Removed extra sign in front of -260
It becomes -2%2Ax%2B3%2A%28-x%2B180%29-highlight_green%28+260+%29=0.
Look at -2%2Ax%2Bhighlight_red%28+3%2A%28-x%2B180%29+%29-260=0.
Expanded term 3 by using associative property on %28-x%2B180%29
It becomes -2%2Ax-highlight_green%28+3%2Ax+%29%2Bhighlight_green%28+3%2A180+%29-260=0.
Look at -2%2Ax-3%2Ax%2Bhighlight_red%28+3+%29%2Ahighlight_red%28+180+%29-260=0.
Multiplied numerator integers
It becomes -2%2Ax-3%2Ax%2Bhighlight_green%28+540+%29-260=0.
Look at -2%2Ax-3%2Ax%2Bhighlight_red%28+540+%29-highlight_red%28+260+%29=0.
Added fractions or integers together
It becomes -2%2Ax-3%2Ax%2Bhighlight_green%28+280+%29=0.
Look at -highlight_red%28+2%2Ax+%29-highlight_red%28+3%2Ax+%29%2B280=0.
Eliminated similar terms highlight_red%28+-2%2Ax+%29,highlight_red%28+-3%2Ax+%29 replacing them with highlight_green%28+%28-2-3%29%2Ax+%29
It becomes highlight_green%28+%28-2-3%29%2Ax+%29%2B280=0.
Look at %28-highlight_red%28+2+%29-highlight_red%28+3+%29%29%2Ax%2B280=0.
Added fractions or integers together
It becomes %28highlight_green%28+-5+%29%29%2Ax%2B280=0.
Look at %28highlight_red%28+-5+%29%29%2Ax%2B280=0.
Removed extra sign in front of -5
It becomes %28-highlight_green%28+5+%29%29%2Ax%2B280=0.
Look at highlight_red%28+%28-highlight_red%28+5+%29%29%2Ax+%29%2B280=0.
Remove unneeded parentheses around factor highlight_red%28+5+%29
It becomes -highlight_green%28+5+%29%2Ax%2B280=0.
Look at highlight_red%28+-5%2Ax%2B280+%29=0.
Solved linear equation highlight_red%28+-5%2Ax%2B280=0+%29 equivalent to -5*x+280 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=56.

Universal Simplifier and Solver


Done!



Step 8. ANSWER: The angle is 56 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.

Good luck in your studies!

Respectfully,
Dr J

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
if one-half of the complement of an angle plus three-fourths of the supplement of the angle equals 110, find the measure of the angle.
:
Let x = "the angle"
:
"if one-half of the complement of an angle"
.5(90-x)
:
"three-fourths of the supplement"
.75(180-x)
:
find the measure of the angle.
:
Write the equation for the statement:
"one-half of the complement of an angle plus three-fourths of the supplement of the angle equals 110,"
:
.5(90-x) + .75(180-x) = 110
45 - .5x + 135 - .75x = 110
180 - 1.25x = 110
180 - 110 = +1.25x
x = 70%2F1.25
x = 56 degrees
;
:
See if this is true in the statement:
one-half of the complement of an angle plus three-fourths of the supplement of the angle equals 110,
.5(90-56) + .75(180-56) =
.5(34) + .75(124) =
17 + 93 = 110