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Big Ideas Math: Modeling Real Life, Grade 8

BI

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

4. Rational Numbers

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Exercise 5 Page 399

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

40^(∘), 60^(∘), and 80^(∘)

Practice makes perfect

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!

Interior Angle Measures 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. x^(∘) + (x + 40)^(∘) + 60^(∘) = 180^(∘) Let's solve the equation and find the value of x. For simplicity, we will not write the degree symbol.

x+(x+40)+60 = 180

▼

Solve for x

Remove parentheses

x + x + 40 + 60 = 180

Add terms

2x + 100 = 180

LHS-100=RHS-100

2x = 80

.LHS /2.=.RHS /2.

x = 40

The measure of one of the angles is 40^(∘). To find the other missing measure, we will substitute x=40 in the expression for the remaining angle, (x+40)^(∘). Once again, we will remove the degree symbol for the calculation.

x+40

x= 40

40+40

Add terms

80

The measure of the third angle is 80^(∘).

triangle

Subchapter links

Try It p.396-397

Self-Assessment for Concepts & Skills p.397-398

Review & Refresh p.399

Concepts, Skills, & Problem Solving p.399-400