Atriangle has an angle that measures 80°. the other two angles are in a ratio of 7: 13. what are the measures of those two angles?

You can make a system of equation using the fact that all angles in a triangle need to add up to 180 and that 7:13 can be thought of as 7/13.
lets make one angle a and the other angle b.

a+b=100  (a+b+80=180)
a÷b=7/13

You can solve for a in the second equation to get a=7b/13 and then you can substitute that in for a in the first equation to get (7b/13)+b=100 and then solve for b as follows.
(7/13)b+b=100
b(7/13+1)=100
b(20/13)=100
b=65
You can then solve for a in from plugging in b to the first equation to get a=35.
Therefore the 2 other angles are 35° and 65°. 

You can prove this by showing that 35+65+80=180 and that 35/65=7/13.

I hope this helps.  Let me know in the comments if anything is unclear.