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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

Chapter Review

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Exercise 5 Page 290

Consider the Triangle Angle-Sum Theorem.

35^(∘), 55^(∘)

Practice makes perfect

Let's analyze the given triangle.

According to the Triangle Angle-Sum Theorem the measures of the interior angles of a triangle add to 180^(∘). Since one of the angles is a right angle, the acute angles are complementary. In this case, it means that (7x+6) and (6x-7) add to 90. (7x+6)+(6x-7)=90 We will now solve the above equation for x.

7x+6+6x-7=90

Add and subtract terms

13x-1=90

LHS+1=RHS+1

13x=91

.LHS /13.=.RHS /13.

x=7

Once we know the value of x, we can find the measures of acute angles. ccc (7x+6)^(∘) &→& (7( 7)+6)^(∘)&→& 55^(∘) (6x-7)^(∘) &→& (6( 7)-7)^(∘)&→& 35^(∘) Therefore, the measures of the acute angles are 35^(∘) and 55^(∘).