Question

NP bisects 4MNO. The measure of angle 4PNO is x+15, and the measure of angle 4MNO is 4x-70. What is the measure of angle 4MNP?

a) 50
b) 65
c) 100
d) 130

Answer 1

The measure of angle 4MNP is (a) 50°. We found this by setting up an equation based on the information that NP bisects angle 4MNO, yielding the value for x, which is 50.

Step-by-step explanation:

The student asks to find the measure of angle 4MNP, given that NP bisects angle 4MNO and that the measures of angles 4PNO and 4MNO are x+15 and 4x-70, respectively. Since NP bisects angle 4MNO, it means that angles 4MNP and 4PNO are congruent.

Firstly, we can set up the equation for the angles being congruent: (x + 15) = (4x - 70) / 2. Solving for x, we get:

1. x + 15 = 2x - 35
2. x = 50

Thus, the measure of angle 4MNP is 50, which corresponds to option (a) 50°.