You can put this solution on YOUR website! find the measure of an angle if it's supplement measures 15 degrees less than 4 times it's complement
Let the required angle be A degrees
Let its supplement be S degrees
and complement be C degrees.
Then we have
A+S = 180 ----(1)And
A+C = 90 ----(2)
supplement measures 15 degrees less than 4 times it's complement
That is S measures 15 less than 4C
That is S = 4C-15 ----(3)
Now (1) - (2) gives
(A-A) +(S-C) = 180-90
0 +(S-C) = 90
(S-C) = 90
That is S = 90+C ----(4)
From (3) and (4)
4C-15 = 90+C
4C-C =90+15
3C = 105
C = 105/3 = 35
Putting C = 35 in (2)
A+C = 90
A+35= 90
A =90-35 = 55
Answer: A = 55 degrees. That is the required angle is 55 degrees
Verification:From (1) S = 180-A = 180-55 = 125 and
From (3) S = 4C-15 = 4X35 - 15 = 140-15 = 125 which is correct from above
Therefore our angle A is correct
Note: Why did we do (1)-(2)?
Answer: To get an equation in S and C so that
we can make it converse with (3) which is given in S and C
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