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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 10 Page 430

Find the corresponding remote interior angles to ∠ 5.

∠ 7 and ∠ 8

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, ∠ 5 is an exterior angle to △ BCD. Because angles ∠ 7 and ∠ 8 do not share a vertex or corner of the triangle with ∠ 5, these are the corresponding remote interior angles. Let's now 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.

By this theorem, we can conclude that the measure of ∠ 5 is greater than the measures of ∠ 7 and ∠ 8. In other words, m∠ 7 and m ∠ 8 are less than m∠ 5.

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Exercises p.430-433