You can put this solution on YOUR website!
First, I'm going to rename the angles so that they're easier to deal with. Angle 1 will now be angle A, and angle 2 will now be angle B.
Supplementary angles add up to 180 degrees, so A+B=180.
The measure of B is 17 times the measure of A. "Is" means "equals", so B=17*A, or just B=17A. That means that instead of saying B, I can say 17A. Going back to the first equation, we can now say A+17A=180. Combine like terms and get 18A=180. Divide by 18 on both sides, and A=10 degrees. Since B=17A, and A is 10, B=17*10=170, so B=170 degrees.