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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

1. Angles of Triangles

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Exercise 25 Page 237

What is the sum of the interior angles of a triangle?

16.5^(∘) and 73.5^(∘)

Practice makes perfect

First, we will illustrate the given information in a diagram. Let x be the measure of the smaller acute angle. Therefore, the measure of the larger acute angle is 3 times the sum of x and 8. This means that its measure is 3(x+8).

According to the Corollary to the Triangle Sum Theorem, the acute angles of a right triangle are complementary. 3(x+8)+x= 90 Let's solve this equation.

3(x+8)+x=90

Distribute 3

3x+24+x=90

Add terms

4x+24=90

LHS-24=RHS-24

4x=66

.LHS /4.=.RHS /4.

x=16.5

The measure of the smaller acute angle is x=16.5. Now, we can find the measure of the greater acute angle. 3(x+8) ⇒ 3(16.5+8) = 73.5^(∘)

Subchapter links

Communicate Your Answer p.231

Monitoring Progress p.232-235

Exercises p.236-238