Exercise 27 Page 349

We are asked to determine which angle out of ∠ 3, ∠ 11, and ∠ 12 has the greatest measure.

Notice that ∠ 11 and ∠ 12 are interior angles, while ∠ 3 is an exterior angle of the same triangle. Moreover, because ∠ 11 and ∠ 12 do not share a vertex or corner of a triangle with ∠ 3, they are corresponding remote angles of ∠ 3. Now, let's review the Exterior Angle Inequality Theorem.

According to this theorem, ∠ 3 is greater than ∠ 11 and ∠ 12. Therefore, ∠ 3 is the greatest angle out of these three angles.