The side MN of $$\triangle$$LMN is produced to X. If $$\angle$$LNX = $$117^\circ$$ and $$\angle$$M = $$\frac{1}{2} \angle$$L, then $$\angle$$L is:

Given, $$\angle$$LNX = $$117^\circ$$ and $$\angle$$M = $$\frac{1}{2} \angle$$L

In $$\triangle$$LMN,

The exterior angle LNX is equal to the sum of the opposite interior angles L and M.

$$\Rightarrow$$  $$\angle$$LNX = $$\angle$$L + $$\angle$$M

$$\Rightarrow$$  $$117^\circ$$ = $$\angle$$L + $$\frac{1}{2} \angle$$L

$$\Rightarrow$$  $$117^\circ$$ = $$\frac{3}{2} \angle$$L

$$\Rightarrow$$  $$\angle$$L =  $$78^\circ$$

Hence, the correct answer is Option A