Hello!
First, let's take a look at the two angles together. We can see that the two angles, when the measures are combined, add up to form a line, DEF. We can therefore see that the two angles DEG and GEF must add up to 180 degrees, as the measure of a line is 180 degrees.
Therefore, we can create our equation.
(7x - 3) + (12x - 7) = 180
Now, solve for x.
7x - 3 + 12x - 7 = 180
19x = 190
x = 10
Finally, substitute x into the angle measures to find the integer measurements.
Angle DEG: 7x - 3
7 * 10 - 3
70 - 3
67 degrees
Angle GEF: 12x - 7
12 * 10 - 7
120 - 7
113 degrees
Just to be sure, add up the angle measurements to make sure they equal 180. 67 + 113 = 180, which means we did our math correctly.
Hope this helps!