body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

3. Inequalities in One Triangle

Continue to next subchapter

Exercise 13 Page 430

Which angles are corresponding remote angles to ∠ 7?

∠ 5 and ∠ 9

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, ∠ 7 is an interior angle of △ BCD. Because ∠ 5 and ∠ 9 do 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 ∠ 5 and ∠ 9 have greater measures than ∠ 7.

Subchapter links

Exercises p.430-433