SOLUTION: Please help me solve this problem: The measure of the supplement of an angle is 3 times as great as the measure of the angle's complement. Find the measure of the angle. Please

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Question 220931: Please help me solve this problem: The measure of the supplement of an angle is 3 times as great as the measure of the angle's complement. Find the measure of the angle.
Please help me solve this problem: The difference between the measures of the angle and its complement is 14. Find the measure of the angle and its complement.
Please help me solve this problem: Find the measure of an angle if it is 12 less than twice the measure of its complement.
Please help me solve this problem: If a point C is equidistant from points A and B, then point C is the midpoint of the segment that joins A and B.
Thank you for your time and help. Can you please explain them step by step? Sorry and thank you again.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
All you have to know here is the definition of "complement and supplement"
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The measure of the supplement of an angle is 3 times as great as the measure of the angle's complement.
Find the measure of the angle.
:
let x = "the angle"
supplement = 180-x
complement = 90-x
:
The equation for what it says (the word "is" usually means =):
180-x = 3(90-x)
180 - x = 270 - 3x
-x + 3x = 270 - 180
2x = 90
x = 90%2F2
x = 45 degrees
You can check the solution in the original equation
;
:
The difference between the measures of the angle and its complement is 14.
Find the measure of the angle and its complement.
x - (90-x) = 14
x - 90 + x = 14
x + x = 14 + 90
2x = 104
x = 52 degrees
Check solution in original equation
:
:
Find the measure of an angle if it is 12 less than twice the measure of its complement.
x = 2(90-x) - 12
x = 180 - 2x - 12
x + 2x = 180 - 12
3x = 168
x = 168%2F3
x = 56 degrees
:
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If a point C is equidistant from points A and B, then point C is the midpoint of the segment that joins A and B. OK, I agree with that!