Exercise 21 Page 340

Consider the given diagram.

We want to find each measure on the diagram. Let's do it one at time!

Finding x

First, we will use the information given to set up and solve an equation for x. Notice that on the diagram we are given the measure of an exterior angle of triangle ABC. We are also given expressions for two remote interior angles at A and B. Then, we can use the Exterior Angle Theorem.

This theorem lets us set up and solve an equation for x. FOr simplicity, let's disregard the degree symbol for this calculation.

The value of x on the diagram is 56^(∘).

Finding m∠ ABC

We are asked to find the measure of ∠ ABC. We can do this by substituting the value we found for x in the expression given on the diagram for m∠ ABC. We will again disregard the degree symbol until the end.

The measure of ∠ ABC is 51^(∘).