We can find this answer by remembering the laws about opposite angles and their sums. We know that since 1 and 2 are opposite angles, they must be equal to each other. Therefore, we can set them equal to each other to solve for x.
Solving For x
x+5=6x-30
-x -x
5=5x-30
+30 +30
35=5x
/5 /5
7=x
Now that we know x=7, we can substitute that value in for x in the angle measurements.
Angle 1
x+5
7+5=12
Angle 2
6x-30
6*7-30=12
We know that we have the correct x-value because both angles are equal. Therefore, we know that the measure of both angles is 12 degrees.