PQR is a triangle. The bisectors of the internal angle $$ \angle LQ $$ and external angle $$ \angle LR $$ intersect at M. If $$ \angle LQMR = 40^\circ $$, then $$ \angle LP $$ is:

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#### Step 1: Understand the Problem
The internal angle bisector of $$ \angle LQ $$ and the external angle bisector of $$ \angle LR $$ intersect at point M such that:  
$$
\angle LQMR = 40^\circ.
$$

#### Step 2: Use Angle Bisector Theorem and Triangle Properties
By the **angle bisector theorem** and the properties of triangle angle sums, we know:  
$$
\angle LP + \angle LQ + \angle LR = 180^\circ.
$$

#### Step 3: Complementary Angle Relation
Since the sum of $$ \angle LQMR $$ with the angles at point M must complement the triangle's angle properties, solving through geometry leads to:  
$$
\angle LP = 80^\circ.
$$

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Thus, the value of $$ \angle LP $$ is **80°**, making Option **2** correct.

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