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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Inequalities in One Triangle

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Exercise 12 Page 430

Which angles are corresponding remote angles to ∠ 8?

∠ 2 and ∠ 5

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, ∠ 8 is an interior angle of △ BCD. Because ∠ 5 and ∠ 2 does not share a vertex or corner of △ BCD, they are 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 ∠ 2 and ∠ 5 have greater measures than ∠ 8.

Extra

Interior Angles of △ ACD

Note that ∠ 8 is also an interior angle of △ ACD. However, we are not given any corresponding remote angles to ∠ 8 in this triangle.

Subchapter links

Exercises p.430-433