Final answer:
To find the value of x when angles 2M and ZN are supplementary with mzM = 37°, we set up the equation 37 + 13x = 180, solve for x, and find that x = 11.
Step-by-step explanation:
To find the value of x and the m of angle 2N, we can use the fact that 2M and ZN are supplementary angles, meaning their measures add up to 180°.
We are given that the measure of angle mzM is 37°.
Since 2M and ZN are supplementary, we can set up the equation: 37 + (13x) = 180.
Solving this equation will allow us to find the value of x, and then substitute it back into the expression for angle 2N to find its measure.
37 + (13x) = 180
Subtracting 37 from both sides: (13x) = 180 - 37 = 143
Dividing both sides by 13: x = 143/13 = 11
Substituting the value of x back into the expression for angle 2N: m2N = 13x = 13(11) = 143°