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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

Chapter Review

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Exercise 4 Page 290

Consider the Triangle Angle-Sum Theorem.

42^(∘), 48^(∘)

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 8x and 7x add to 90. 8x+7x=90 We will now solve the above equation for x.

8x+7x=90

Add terms

15x=90

.LHS /15.=.RHS /15.

x=6

Once we know the value of x, we can find the measures of acute angles. ccc 8x^(∘) &→& 8( 6)^(∘)&→& 48^(∘) 7x^(∘) &→& 7( 6)^(∘)&→& 42^(∘) Therefore, the measures of the acute angles are 42^(∘) and 48^(∘).