Final answer:
The measure of angle LMS is found by subtracting the sum of angles SMN and LMN from 180 degrees, reflecting the sum of angles on a straight line. The calculation gives a result of 82 degrees, suggesting a possible typo in the provided answer choices.
Step-by-step explanation:
The question asks us to find the measure of angle LMS, when given the measures of angle SMN and angle LMN. Assuming that point M is where the angles intersect, forming a straight line with the angles LMS and SMN, we can use the fact that the sum of angles on a straight line equals 180 degrees. The m ∠LMS can be found by subtracting the sum of m ∠SMN and m ∠LMN from 180°.
m ∠LMS = 180° - (m ∠SMN + m ∠LMN)
First, add the measures given for angles SMN and LMN:
m ∠SMN + m ∠LMN = 36° + 62° = 98°
Now, subtract this sum from 180°:
m ∠LMS = 180° - 98° = 82°
Therefore, the measure of bwhich is not one of the options provided, possibly due to a typo in the original question or answer choices. In a real context, it is important to double-check the problem set and the answer choices in such a case.