SOLUTION: The supplementary angle is 30 more than 4 times of a complementary angle. What is the complementary angle measure?

Algebra ->  Angles -> SOLUTION: The supplementary angle is 30 more than 4 times of a complementary angle. What is the complementary angle measure?      Log On


   

Question 549460: The supplementary angle is 30 more than 4 times of a complementary angle. What is the complementary angle measure?
Answer by TutorDelphia(193) About Me  (Show Source):
You can put this solution on YOUR website!
Supplementary is when two angles add up to be 180 degrees (and form a straight line)
Complementary is when they add up to 90 degrees
So if our angle is y
we know that 180-y=30+4*(90-y)
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: y=70.
  • Graphical form: Equation 180-y=30%2B4%2A%2890-y%29 was fully solved.
  • Text form: 180-y=30+4*(90-y) simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+180-y=30%2B4%2A%2890-y%29+%29
    For tutors: simplify_cartoon( 180-y=30+4*(90-y) )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+180+%29-y=30%2B4%2A%2890-y%29.
Moved 180 to the right of expression
It becomes -y%2Bhighlight_green%28+180+%29=30%2B4%2A%2890-y%29.
Look at -y%2B180=30%2B4%2A%28highlight_red%28+90+%29-y%29.
Moved 90 to the right of expression
It becomes -y%2B180=30%2B4%2A%28-y%2Bhighlight_green%28+90+%29%29.
Look at -y%2B180=highlight_red%28+30+%29%2B4%2A%28-y%2B90%29.
Moved 30 to the right of expression
It becomes -y%2B180=4%2A%28-y%2B90%29%2Bhighlight_green%28+30+%29.
Look at -y%2B180=highlight_red%28+4%2A%28-y%2B90%29%2B30+%29.
Moved these terms to the left highlight_green%28+-4%2A%28-y%2B90%29+%29,highlight_green%28+-30+%29
It becomes -y%2B180-highlight_green%28+4%2A%28-y%2B90%29+%29-highlight_green%28+30+%29=0.
Look at -y%2Bhighlight_red%28+180+%29-4%2A%28-y%2B90%29-highlight_red%28+30+%29=0.
Added fractions or integers together
It becomes -y%2Bhighlight_green%28+150+%29-4%2A%28-y%2B90%29=0.
Look at -y%2Bhighlight_red%28+150+%29-4%2A%28-y%2B90%29=0.
Moved 150 to the right of expression
It becomes -y-4%2A%28-y%2B90%29%2Bhighlight_green%28+150+%29=0.
Look at -y-highlight_red%28+4%2A%28-y%2B90%29+%29%2B150=0.
Expanded term -4 by using associative property on %28-y%2B90%29
It becomes -y%2Bhighlight_green%28+4%2Ay+%29-highlight_green%28+4%2A90+%29%2B150=0.
Look at -y%2B4%2Ay-highlight_red%28+4+%29%2Ahighlight_red%28+90+%29%2B150=0.
Multiplied numerator integers
It becomes -y%2B4%2Ay-highlight_green%28+360+%29%2B150=0.
Look at -y%2B4%2Ay-highlight_red%28+360+%29%2Bhighlight_red%28+150+%29=0.
Added fractions or integers together
It becomes -y%2B4%2Ay%2Bhighlight_green%28+-210+%29=0.
Look at -y%2B4%2Ay%2Bhighlight_red%28+-210+%29=0.
Removed extra sign in front of -210
It becomes -y%2B4%2Ay-highlight_green%28+210+%29=0.
Look at -highlight_red%28+y+%29%2Bhighlight_red%28+4%2Ay+%29-210=0.
Eliminated similar terms highlight_red%28+-y+%29,highlight_red%28+4%2Ay+%29 replacing them with highlight_green%28+%28-1%2B4%29%2Ay+%29
It becomes highlight_green%28+%28-1%2B4%29%2Ay+%29-210=0.
Look at %28-highlight_red%28+1+%29%2Bhighlight_red%28+4+%29%29%2Ay-210=0.
Added fractions or integers together
It becomes %28highlight_green%28+3+%29%29%2Ay-210=0.
Look at highlight_red%28+%28highlight_red%28+3+%29%29%2Ay+%29-210=0.
Remove unneeded parentheses around factor highlight_red%28+3+%29
It becomes highlight_green%28+3+%29%2Ay-210=0.
Look at highlight_red%28+3%2Ay-210+%29=0.
Solved linear equation highlight_red%28+3%2Ay-210=0+%29 equivalent to 3*y-210 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: y=70.

Universal Simplifier and Solver


Done!

So we find y=70
but we are asked for the complementary angle so that would be 90-y or 20 degrees