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 26 Page 431

Use the Exterior Angle Inequality Theorem.

∠ 7

Practice makes perfect

We are asked to determine which angle out of ∠ 7, ∠ 4, and ∠ 5 has the greatest measure.

Notice that ∠ 4 and ∠ 5 are interior angles, while ∠ 7 is an exterior angle of the same triangle. Moreover, because ∠ 4 and ∠ 5 do not share a vertex or corner of a triangle with ∠ 7, they are corresponding remote angles of ∠ 7. Now, let's review 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.

According to this theorem, ∠ 7 is greater than ∠ 4 and ∠ 5. Therefore, ∠ 7 is the greatest angle out of these three angles.

Subchapter links

Exercises p.430-433