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McGraw Hill Integrated II, 2012 View details

3. Inequalities in One Triangle

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Exercise 8 Page 430

Which angles are corresponding remote angles to ∠ 2?

∠ 4

Practice makes perfect

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, ∠ 2 is an interior angle of △ ABD. Because ∠ 4 does not share a vertex or corner of the triangle with ∠ 2, it is one of the corresponding remote angles. Now, let's recall 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.

This theorem allows us to conclude that ∠ 4 has a greater measure than ∠ 2.