SOLUTION: Hi there!:) I would like to ask some help with my word problem solving...If one could please help me with it.. The problem is: The measure of an angle and its complement diffe

Question 466528: Hi there!:)
I would like to ask some help with my word problem solving...If one could please help me with it..
The problem is:
The measure of an angle and its complement differ by 22. Find the angle and its complement.
I would like to thank the one who would help me in advance!:D
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
The problem is:
The measure of an angle and its complement differ by 22. Find the angle and its complement.
the answer is:
if the angle is equal to x, then the complement of the angle is equal to 90 - x.
that's because the sume of an angle plus its complement must always be equal to 90 degrees.
the problem states that the angle and its complement differ by 22.
this means that, if the angle is equal to x, then the angle's complement is either equal to x + 22, or x - 22.
let's assume that the complement of the angle is equal to x + 22.
since the angle plus its complement must always be equal to 90 degrees, then we get the equation:
x + (x + 22) = 90
this results in 2x + 22 = 90.
subtract 22 from both sides of this equation to get:
2x = 68
divide both sides of this equation and you get x = 34.
this makes x + 22 = 56
the sum of 34 and 56 = 90 so we're good.
let's assume that the complement of the angle is equal to x - 22.
since the angle plus its complement must always be equal to 90 degrees, then we get the equation:
x + (x - 22) = 90
this results in 2x - 22 = 90.
add 22 to both sides of this equation and you get 2x = 112
divide both sides of this equation by 2 and you get x = 56
this makes x - 22 = 34.
the sum of 56 + 34 = 90 so we're good.
either way you get an angle of 34 degrees and an angle of 56 degrees.
if you pick your angle as being 34, then the complement is 56.
if you pick your angle as being 56, then the complement is 34.
the angle plus its complement must always be equal to 90 degrees.
that's the rule that allows you to solve this problem.

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