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Big Ideas Math: Modeling Real Life, Grade 8

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Big Ideas Math: Modeling Real Life, Grade 8 View details

Practice Test

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Exercise 6 Page 134

The sum of the measures of the interior angles of a triangle is 180^(∘).

68^(∘), 68^(∘), and 44^(∘)

We want to find the measures of the angles in the given triangle.

triangle

To find these angle measures, we will first recall a key piece of information!

Angle Sum of a Triangle
The sum of the measures of the interior angles of a triangle is 180^(∘).

With this rule, we can write an equation connecting the measures of the angles of our triangle. 68^(∘)+ x^(∘)+ (x-24)^(∘)=180^(∘) Let's solve the equation and find the value of x. For simplicity, we will not write the degree symbol.

68+x+(x-24)=180

▼

Solve for x

Remove parentheses

68+x+x-24=180

CommutativePropAdd

Commutative Property of Addition

x+x+68-24=180

Add and subtract terms

2x+44=180

LHS-44=RHS-44

2x=136

.LHS /2.=.RHS /2.

2x/2=136/2

Calculate quotient

x=68

The measure of one of the angles is 68^(∘). To find the other missing measure, we will substitute x= 68 in the expression for the remaining angle, (x-24)^(∘). Once again, we will remove the degree symbol for the calculation.

x-24

x= 68

68-24

Subtract term

44

The measure of the third angle is 44^(∘).

triangle

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