Final answer:
If MN bisects PMR, the measures of PMN and NMR will be equal. The measure of ONE is given as 102°. Setting up an equation, we find that the measures of PMN and NMR are both 39°.
Step-by-step explanation:
If MN bisects PMR, then the measure of PMN and NMR will be equal since they are opposite angles formed by the bisector. Let's call the measure of PMN and NMR as x. The measure of ONE is given as 102°. Since MN bisects PMR, the measure of PMR will be twice the measure of PMN and NMR, so it can be written as 2x. The sum of angles in a triangle is 180°, so we can set up an equation:
x + x + 102° = 180°
2x + 102° = 180°
Subtract 102° from both sides:
2x = 78°
Divide both sides by 2 to solve for x:
x = 39°
Therefore, the measures of PMN and NMR are both 39°.