Geometry

The answer is D. LM = 71 and LN = 92.

1. First, write an equation based on the segment - addition postulate:

Since , with , , and , the equation is .

2. Then, simplify the left - hand side of the equation:

Combine like terms: . So the equation becomes .

3. Next, solve for :

Subtract from both sides: , which gives .

Subtract 50 from both sides:

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