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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 26 Page 237

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

38^(∘) and 52^(∘)

Practice makes perfect

First, we will illustrate the given information in a diagram. Let x be the measure of one acute angle. Therefore, the measure of the other acute angle is 2 times the difference of x and 12. This means that its measure is 2(x-12).

According to the Corollary to the Triangle Sum Theorem, the acute angles of a right triangle are complementary. 2(x-12)+x= 90 Let's solve this equation.

2(x-12)+x=90

Distribute 2

2x-24+x=90

Add terms

3x-24=90

LHS+24=RHS+24

3x=114

.LHS /3.=.RHS /3.

x=38

The measure of one of the acute angles is x=38. Now, we can find the measure of the other acute angle. 2(x-12)^(∘) ⇒ 2(38-12) = 52^(∘)

Subchapter links

Communicate Your Answer p.231

Monitoring Progress p.232-235

Exercises p.236-238