Question

the measure of an angle is 50 more than the measure of its suplement. what is the measure of the smaller angle?

Answer 1

to solve this, we can set up 2 equations
x= angle 1
y= angle 2

x + 50 = y (measure of angle y is 50 more than measure of angle x)
x + y = 180 (angles are supplements, which means they add up to 180 degrees)

we are given what y is equal to (x+50) so, we can plug this value in for y in the second equation and solve for x

x + y = 180
x +(x + 50) =180
2x + 50 = 180
2x = 130
x = 65 degrees

now that we know what x is equal to, we can plug 65 into either equation for x and solve for y

65 + y =180
y = 115 degrees

now that we know the measure of both angles, we can conclude that the measure of the smaller angle is 65 degrees

hope this helped!

Answer 2

Hey!

A supplementary angle adds up to 180°. You can make an equation


`x + (x + 50) = 180`

Let's simplify that:


`2x + 50 = 180`

Switch it around and it becomes:


`180 - 50 = 2x`
The sign changes when moved to the other side.

Subtract 50 from 180


`180 - 50 = 130`


`130 = 2x`

Divide both sides by 2


`(130)/(2) = (2x)/(2)`


`\framebox{x = 65 \°}`