Exercise 4 Page 339

Identify exterior and interior angles of the given triangle.

101^(∘)

Practice makes perfect

We are asked to find the measure of ∠ MPQ. Let's start by marking this angle on the diagram.

Notice that this angle is an exterior angle of triangle △ MPQ and that the measures of the two remote interior angles are given on the diagram. To find the desired measure, we will use the Exterior Angle Theorem.

Exterior Angle Theorem
The measure of an exterior angle is the sum of the measures of the two remote interior angles.

We can use this theorem to set up and solve an equation for m∠ MPQ. m∠ MPQ=m∠ PMN+m∠ MNP Now, we will substitute m∠ PMN = 56^(∘) and m∠ MNP = 45^(∘) into the equation and calculate the measure of angle MPQ. Let's do it!

m∠ MPQ=m∠ PMN+m∠ MNP

SubstituteII

m∠ PMN= 56^(∘), m∠ MNP= 45^(∘)

m∠ MPQ= 56^(∘)+ 45^(∘)

AddTerms

Add terms

m∠ MPQ=101^(∘)

The measure of ∠ MPQ is 101^(∘).