Weare given two supplementary angles (recall that supplementary angles add up to give 180 degrees) in expressions that contain a variable "x":
m angleM = 6 x + 3
m angle N = 2 x - 7
So we use the property that the addition of these two supplementary angles must give 180 degrees:
6 x + 3 + 2 x - 7 = 180
and solve for "x":
6 x + 2 x + 3 - 7 = 180
8 x - 4 = 180
8 x = 184
x = 184 /8
x = 23 degrees
Then we can find now the measure of angle M as:
M = 6 x + 3 = 6 * 23 + 3 = 141
N = 2 x - 7 = 2 * 23 - 7 = 39
Therefore this agrees with the third answer listed in the problem.