Question 472256

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).
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angles whose measure amounts to 180 degree are called supplementary angles.
thus,
supplement of angle x is (180-x)
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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)
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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.