Find the measure of angle 7.
measure of angle 7 = 2x+15
measure of angle 8 = 3x

The
the main rules of angles are:
if a and b are opposite angles, then  measure of a = measure of b
sometimes, two angles are called vertical, if it is opposite and each value of the angle must be equal

in our case, 6 and 8 are vertical angles, and so are 5 and 7 
so measure 6 = measure 8 and
measure 7 = measure 5

besides, measure 8 +  measure 7= 180° (a straight angle)
it means 8x +  2x+15 = 180° 
10x = 180° -15, this implies x = 180° -15 / 10 = 16.5°

finally, measure of angle 7 = 2x+15 = 2 (16.5) +15 = 48°