Answer: Choice B.
The statement is valid because the measure of the vertices located in the center of the pentagon is the quotient of 360 and 5, and the sum of two base angles in the given isosceles triangle is 108.
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Step-by-step explanation:
Check out the diagram below. I have added x and y such that
x = base angle
y = vertex angle (located adjacent to center of polygon)
The pentagon is sliced up like a cake into 5 equal portions. Each vertex angle is y = 360/5 = 72 degrees.
The two base angles x must add with the vertex angle y to get 180
(angle1)+(angle2)+(angle3) = 180
x+x+y = 180
2x+y = 180
2x+72 = 180
2x = 180-72
2x = 108
This is true for any one of the five triangles. Notice that for angle LMN, we can divide it into LMQ and QMN where Q is the center of the polygon. Both of these angles are x. Since we've shown 2x = 108, we can see that LMN must also be 108 as well.
Choice A is close, but we wouldn't use the exterior angle theorem. Choice B is the better answer.