SOLUTION: An angle�s measure is 3 times the measure of its complement

Question 97618This question is from textbook Holt Geometry Texas
: An angle�s measure is 3 times the measure of its complement This question is from textbook Holt Geometry Texas

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given
.
An unknown angle. Call its measure m
.
Known:
.
The measure of the angle plus the measure of its complement (call the measure of its complement "c")
totals to 90 degrees. In equation form this is:
.
m + c = 90
.
But the problem tells you that m (the measure of the angle) is 3 times the measure of the complement.
In equation form this is:
.
m = 3c
.
You can now go back to the equation
.
m + c = 90
.
and for m you can substitute the equivalent "3c" to make the equation become
.
3c + c = 90
.
The terms on the left side combine to give:
.
4c = 90
.
Solve for c (the measure of the complement) by dividing both sides by 4 to get:
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c = 90/4 = 22.5 degrees.
.
22.5 degrees is the measure of the complement. And since the measure of the angle is
three times as much as c, m must be equal to 3 times 22.5 degrees which is 67.5 degrees.
.
Check by noting that 67.5 degrees is 3 times 22.5 degrees and also that 67.5 + 22.5 = 90 degrees.
.
Hope this helps you to understand the problem a little better.
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