the answer:
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°
