Posted by **rhodora** on Friday, October 11, 2013 at 9:05am.

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.

- plss answer fast math algebra -
**Reiny**, Friday, October 11, 2013 at 9:46am
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

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