Exercise 25 Page 431

We are asked to determine which angle out of ∠ 2, ∠ 4, and ∠ 6 has the greatest measure.

Notice that ∠ 4 and ∠ 6 are interior angles, while ∠ 2 is an exterior angle of the same triangle. Moreover, because ∠ 4 and ∠ 6 do not share a vertex or corner of a triangle with ∠ 2, they are corresponding remote angles of ∠ 2. Now, let's review the Exterior Angle Inequality Theorem.

According to this theorem, ∠ 2 is greater than ∠ 4 and ∠ 6. Therefore, ∠ 2 is the greatest angle out of these three angles.