Exercise 53 Page 343

Let's label all interior and exterior angles of the triangle and put the given measures on the diagram.

We will find the exterior angle measures one at a time.

Finding m∠ 4

Notice that angles ∠ 1 and ∠ 2 together form a straight angle, so their measures add to 180^(∘).

Since the measure of ∠ 1 is given, this allows us to set up and solve an equation for m∠ 4.

Finding m∠ 5

We can similarly find the measure of ∠ 5.

Finding m∠ 6

Since the measure of the interior angle adjacent to ∠ 6 is not given, we use a different approach to find its measure. Notice that the measures of the two remote interior angles are given.

The Exterior Angle Theorem tells us about the relationship between these angles. This allows us to find the measure of ∠ 6.

Summary

The diagram below shows all exterior angle measures of the triangle.