SOLUTION: The sum of the measure of two acute angles is 120. the supplement of the smaller angle is 10 more than six times the complement of the larger angle. find the measures of the two ac

Question 472256: The sum of the measure of two acute angles is 120. the supplement of the smaller angle is 10 more than six times the complement of the larger angle. find the measures of the two acute angles.
Answer by dudeantariksh(10) (Show Source): You can put this solution on YOUR website!

Hey. hie there!
let us assume the smaller of the acute angls to be x.
as the two angles amount to 120,
the other angle is (120-x).
_______________________________________________________________________________
angles whose measure amounts to 180 degree are called supplementary angles.
thus,
supplement of angle x is (180-x)
_______________________________________________________________________________
angles whose measures amount to 90 degres are called complementary angles.
thus,
complement of angle (120-x) will be 90-(120-x)
= 90-120+x
= -30+x
= (x-30)
________________________________________________________________________________
our problem says that
the supplement of the smaller angle is 10 more than six times the complement of the larger angle.
in other words i can say that
(180-x)=6(x-30)+10
that is,
180-x= 6x-180+10
therefore,
180-x=6x-170.................adding like terms.
therefore,
180+170=6x+x................ collecting like terms on one side.
therefore,
350=7x
dividing both sides by 7, we get,
x=50
if x = smaller angle=50,
120-x = larger angle = 120-50
= 70
therefore the two angles are 70 and 50.
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