SOLUTION: The supplement of an angle is 60 degrees less than the supplement of the complement. Find the measure of the complement.
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Question 54048This question is from textbook
: The supplement of an angle is 60 degrees less than the supplement of the complement. Find the measure of the complement. This question is from textbook
You can put this solution on YOUR website! Q.The supplement of an angle is 60 degrees less than the supplement of the complement. Find the measure of the complement.
ANS:
Let the angle be X .
Then by definition :
supplement of an angle is the angle which when added to the given angle completes it equal to 180 degrees.
complement of an angle is the angle which when added to the given angle completes 90 degrees.
let y be the supplement of x and m be the complement of x.
hence from the definition ,
y + x = 180
and m + x = 90
thus y = 180 - x
and m = 90 - x
according to the question , y - 60 = 180 - m
(180 - x) - 60 = 180 - (90 - x)
180 - 60 = 90 + 2* x
x = 30/2 = 15 degrees
hence m = 90 - 15 = 85 degrees
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