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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 4 Page 430

Find the corresponding remote angles to ∠ 9.

∠ 6, ∠ 7, ∠ 1, and ∠ 2

Practice makes perfect

Let's consider the given diagram. For the following explanation to be easier, we will name the vertices of the triangles.

As we can see, ∠ 9 is an exterior angle to △ MLN. Because ∠ 6 and ∠ 7 do not share a vertex or corner of the triangle with ∠ 9, these are the corresponding remote 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 ∠ 9 is greater than the measures of ∠ 6 and ∠ 7. Moreover, ∠ 9 is exterior angle to △ MLK. Because angles ∠ 1 and ∠ 2 also do not share a vertex or corner of the triangle with ∠ 9, these are the corresponding remote angles, whose measure less than m∠ 9.

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Exercises p.430-433