the ratio of the measure of the complementsof two angle is3:4while the ratio of the measure of their supplements is 9:10 find the measure of each angle.

Answer 1

let one angle be x
let the other be y

then their complements are 90-x and 90-y
and their supplements: 180-x and 180-y

(90-x)/(90-y) = 3/4
270 - 3y = 360 - 4x
4x - 3y = 90 , #1

(180-x)/(180-y) = 9/10
1620 - 9y = 1800 - 10x
10x - 9y = 180 , #2

#1 times 3
12x - 9y = 270
subtract #2
2x = 90
x = 45
into #1

180 - 3y = 90
-3y = -90
y = 30

so one angle is 45° and the other is 30°

check:
their complements are 45 and 60
45 : 60 = 3:4
their supplements are 135 and 150
135:150 = 9:10
YEAHHH

Answer 2

the ratio of the complement of an angle to the supplement is 1:7.Find the angle.