Exercise 10 Page 430

Let's start by analyzing the given diagram. For the purposes of the solution, we will name the vertices of the triangles.

As we can see, ∠ 5 is an exterior angle to △ BCD. Because angles ∠ 7 and ∠ 8 do not share a vertex or corner of the triangle with ∠ 5, these are the corresponding remote interior angles. Let's now recall the Exterior Angle Inequality Theorem.

By this theorem, we can conclude that the measure of ∠ 5 is greater than the measures of ∠ 7 and ∠ 8. In other words, m∠ 7 and m ∠ 8 are less than m∠ 5.