Exercise 43 Page 421

Let's make a diagram where we see the rays and the points.

From the exercise, we know that m∠ LMN=76^(∘). Let's mark this angle in the diagram.

The ray MP is in the interior of ∠ LMN. It follows from the Angle Addition Postulate the following equation, where ∠PMN and ∠LMP are the resulting angles from drawing the ray. ∠PMN+∠LMP=∠LMN Since we know that the m∠PMN=36^(∘) we can find m∠LMP. 36^(∘) + m∠LMP = 76^(∘) ⇒ m∠LMP=40^(∘)