modifying above upper L upper O with right pointing arrow bisects ∡NLM, LM = 26, NO = 8, and LN = 18. What is the value of x?

Question

The angles of an isosceles triangle are upper L, upper M, upper N. A ray starts at angle upper L and passes through the upper O side of the triangle. Lower x sits below the label upper O on this side.
(1 point)
Responses

x = 84.5
x = 84.5

x = 58.5
x = 58.5

x = 11.6
x = 11.6

x = 5.5

Answer 1

To solve this problem, we can first use the Law of Sines to find angle ∠OLN.

sin∠OLN / 26 = sin∠NLM / 18
sin∠OLN = (26/18) * sin∠NLM
sin∠OLN = (26/18) * (26/26)
sin∠OLN = 26/18
sin∠OLN = 1.444

Since sin∠OLN = 1.444 is not possible, we know that the triangle formed is not possible and there may be an error in the question.