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McGraw Hill Integrated II, 2012 – Inequalities in One Triangle

∠ 3

Solution

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.

Exterior Angle Inequality Theorem

The measure of an exterior angle of a triangle is greater than the measure of either of its corresponding remote interior angles.

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

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