Exercise 26 Page 431

We are asked to determine which angle out of ∠ 7, ∠ 4, and ∠ 5 has the greatest measure.

Notice that ∠ 4 and ∠ 5 are interior angles, while ∠ 7 is an exterior angle of the same triangle. Moreover, because ∠ 4 and ∠ 5 do not share a vertex or corner of a triangle with ∠ 7, they are corresponding remote angles of ∠ 7. Now, let's review the Exterior Angle Inequality Theorem.

According to this theorem, ∠ 7 is greater than ∠ 4 and ∠ 5. Therefore, ∠ 7 is the greatest angle out of these three angles.