Final answer:
Using the properties of an isosceles triangle and the fact that the sum of angles in any triangle is 180 degrees, we determined that the measure of angle O in triangle MNO is 96 degrees. This is calculated by subtracting the known angles of 42 degrees each from 180 degrees.
Step-by-step explanation:
To find the measure of angle O in triangle MNO, where NO is congruent to MN and the measure of angle M is 42 degrees, we can use the properties of an isosceles triangle. In an isosceles triangle, the angles opposite the congruent sides are also congruent. Since NO is congruent to MN, this means that angle N is also 42 degrees.
Now, the sum of all angles in any triangle is 180 degrees. Therefore, to find the measure of angle O, we subtract the sum of the measures of angles M and N from 180 degrees:
Measure of angle O = 180 degrees - (Measure of angle M + Measure of angle N)
= 180 degrees - (42 degrees + 42 degrees)
= 180 degrees - 84 degrees
= 96 degrees
So, angle O measures 96 degrees, which is not one of the options provided. Hence, there may have been a typo in the question or the provided options.