Exercise 19 Page 547

An extended ratio compares three or more numbers. In an extended ratio a : b : c, the ratio of the first two numbers is a : b, the ratio of the last two numbers is b : c, and the ratio of the first and last numbers is a : c. We want to find the measures of the angles of a triangle that fit the given extended ratio. 10 : 8 : 6 This means that we can express the measures of the angles of the triangle as 10x, 8x, and 6x.

By the Triangle Angle Sum Theorem we know that the sum of the measures of the angles of a triangle is 180^(∘). 10x + 8x + 6x=180 Let's solve this equation and find x.

10x+8x+6x=180

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Solve for x

AddTerms

Add terms

24x=180

DivEqn

.LHS /24.=.RHS /24.

x=180/24

CalcQuot

Calculate quotient

x=7.5

Now, to find the measure of each angle of the triangle we will substitute x= 7.5 into the expressions for each of the angle measures.

Expression	Substitute	Simplify
10x	10( 7.5)	75
8x	8( 7.5)	60
6x	6( 7.5)	45

The measures of the angles are 75^(∘), 60^(∘), and 45^(∘).