Conrad drew 2 angles. three times the measure of angle 1 is 30° more than 5 times the measure of angle 2. the sum of twice the measure of angle 1 and twice the measure of angle 2 is 180°. find the measure of each angle.

Let x= measure of angle 1
Let y= measure of angle 2

This is solving a system of equations

3x=30+ 5y which can also be written

3x-5y=30, and

2x+2y=180
There are a few ways to solve this, like solving for x in one of the equations and plugging it in for x in the other equation, but here is another way:
2(3x-5y)=2*30
3(2x+2y)= 3*180

6x-10y=60
6x+6y=540, and now subtract to get rid of x
0-16y=-480
Y=30
Plug it back in to either equation and you get x=60