The expression m∠ LMP indicates the measure of the angle between two rays, ML and MP. Similarly, the expression m∠ NMP indicates the measure of the angle between rays MN and MP. To find their measures, let's start by identifying the three angles on a diagram.
Looking at the figures, and by the Angle Addition Postulate, we can see that m∠ LMN is equal to the sum of m∠ LMP and m∠ NMP. We can solve for x by creating an equation using the expressions for the two smaller angles and the value of the larger angle. Note that ∠ LMN is a straight angle, which is always equal to 180^(∘).
Having solved the equation,we can calculate the individual angles by substituting x= - 4 into the expressions for the unknown angles.
m∠ LMP &: - 16( - 4) +13 = 77^(∘)
m∠ NMP &: - 20( - 4) +23 = 103^(∘)
