In circle O, MP is a diameter. If m is 6 more than 5 times the measure of, what is m? 139° 145° 151°

The answer is C) 150 degrees

Given that line MP is the diameter of the circle, thus, the measure of arc MP is 180 degrees.

From the circle, line ON is a radius which cuts arc MP at N.

Given that the measure of arc NP is 6 more than the measure of arc MN, let the measure of arc MN be x, then

the measure of arc NP = 6 + 5x

Also, because the two arcs form a linear pair, thus

6 + 5x + x = 180

6 + 6x = 180

6x = 180 - 6 = 174

x = 174 / 6 = 29.

Therefore, the measure of arc NP is 6 + 5 (29) = 6 + 145 = 151 degrees.