help with math questions?

Question

1) The supplement of an angle is 60 degrees less than twice the supplement of the complement of the angle. Find the measure of the complement.

2) The ratio of an angle to its supplement is 3:7. Find the ratio of the angle to its complement.

I dont understand these questions, can someone help me out?

Answer 1

1.suppose y is the complement of an angle x, and z is the supplement of an angle x,then

x+y=90 degrees

x+z=180 degrees.

complement of x as 90 - x,

and the supplement of x as 180 - x.

180 - x = 2*(180 - (90 - x)) - 60, find 90 - x


2.here,x+z=180
x/z=3/7
7x=3z
10/7*z=180
z=180*7/10
z=126
z=3/7*126
z=54

now, x+y=90,
y=90-54
=36

x / (180 - x) = 3 / 7, find x / (90 - x)

Answer 2

The complement of an angle x is the angle y such that x + y = 90. The supplement of an angle x is the angle z such that x + z = 180. Thus, you can also write the complement of x as 90 - x, and the supplement of x as 180 - x. You can use these identities to write algebraic problems for these word problems.

1) 180 - x = 2*(180 - (90 - x)) - 60, find 90 - x
2) x / (180 - x) = 3 / 7, find x / (90 - x)

In both cases, you should solve the initial equation to find x, and then calculate the desired quantity.

Answer 3

I know the answer to the second one.
Let the angle be '3x'. It's supplement is '7x'
3x + 7x = 180
10x = 180
x = 180/10
x = 18
The angle is 3*18 = 54 degrees
It's complement is 90 - 54 = 36 degrees
The ratio of the angle to its complement is 54:36
When simplified, the ratio becomes 3:2