Exercise 4 Page 430

Let's consider the given diagram. For the following explanation to be easier, we will name the vertices of the triangles.

As we can see, ∠ 9 is an exterior angle to △ MLN. Because ∠ 6 and ∠ 7 do not share a vertex or corner of the triangle with ∠ 9, these are the corresponding remote angles. Let's now recall the Exterior Angle Inequality Theorem.

By this theorem, we can conclude that the measure of ∠ 9 is greater than the measures of ∠ 6 and ∠ 7. Moreover, ∠ 9 is exterior angle to △ MLK. Because angles ∠ 1 and ∠ 2 also do not share a vertex or corner of the triangle with ∠ 9, these are the corresponding remote angles, whose measure less than m∠ 9.