SOLUTION: Two angles are complementary. The measure of one angle is 46° more than three times the measure of the other. Find the measure of each angle.

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Question 1158336: Two angles are complementary. The measure of one angle is 46° more than three times the measure of the other. Find the measure of each angle.
Found 2 solutions by greenestamps, Shin123:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


x = smaller angle
3x+46 = measure of larger ("46 more than 3 times the measure of the other")

Complementary means the sum of the angles is 90 degrees:

x%2B%283x%2B46%29+=+90

Solve using basic algebra....

Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
Let the measure of the shorter angle x. The measure of the longer angle is 3x+46. And since the angles are complementary, we have x%2B%283x%2B46%29=90
Solved by pluggable solver: Solve an equation
This is a solution to the equation:
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=11.
  • Graphical form: Equation x%2B%283x%2B46%29=90 was fully solved.
  • Text form: x+(3x+46)=90 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x%2B%283x%2B46%29=90+%29
    For tutors: simplify_cartoon( x+(3x+46)=90 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x%2Bhighlight_red%28+%283%2Ax%2B46%29+%29=90.
Remove unneeded parentheses around terms highlight_red%28+3%2Ax+%29,highlight_red%28+46+%29
It becomes x%2Bhighlight_green%28+3%2Ax+%29%2Bhighlight_green%28+46+%29=90.
Look at highlight_red%28+x+%29%2Bhighlight_red%28+3%2Ax+%29%2B46=90.
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+3%2Ax+%29 replacing them with highlight_green%28+%281%2B3%29%2Ax+%29
It becomes highlight_green%28+%281%2B3%29%2Ax+%29%2B46=90.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+3+%29%29%2Ax%2B46=90.
Added fractions or integers together
It becomes %28highlight_green%28+4+%29%29%2Ax%2B46=90.
Look at highlight_red%28+%28highlight_red%28+4+%29%29%2Ax+%29%2B46=90.
Remove unneeded parentheses around factor highlight_red%28+4+%29
It becomes highlight_green%28+4+%29%2Ax%2B46=90.
Look at 4%2Ax%2B46=highlight_red%28+90+%29.
Moved these terms to the left highlight_green%28+-90+%29
It becomes 4%2Ax%2B46-highlight_green%28+90+%29=0.
Look at 4%2Ax%2Bhighlight_red%28+46+%29-highlight_red%28+90+%29=0.
Added fractions or integers together
It becomes 4%2Ax%2Bhighlight_green%28+-44+%29=0.
Look at 4%2Ax%2Bhighlight_red%28+-44+%29=0.
Removed extra sign in front of -44
It becomes 4%2Ax-highlight_green%28+44+%29=0.
Look at highlight_red%28+4%2Ax-44+%29=0.
Solved linear equation highlight_red%28+4%2Ax-44=0+%29 equivalent to 4*x-44 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=11.

Universal Simplifier and Solver


Done!
0=0;x=11

4x-44=0 turns into 4x=44. Dividing both sides by 4 gives x=11. 3x+46=11*3+46=79 degrees. So the angles are 11%5Eo and 79%5Eo.