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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

2. Angles of Triangles

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Exercise 3 Page 113

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

70^(∘)

Practice makes perfect

We are given a triangle and asked to find the measure of the exterior angle.

triangle

To do so, let's recall the Exterior Angle Measures of a Triangle Theorem.

Exterior Angle Measures of a Triangle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

We will now identify the exterior angle and the two nonadjacent interior angles.

triangle

We can see that the measure of the exterior angle is y^(∘) and the measures of the nonadjacent interior angles are 40^(∘) and 30^(∘). By the Exterior Angle Measures of a Triangle Theorem, we can write an equation in terms of y. y^(∘)= 40^(∘)+ 30^(∘) Let's solve the equation! For simplicity, we will not write the degree symbol while solving.

y=40+30

Add terms

y=70

The measure of the exterior angle is 70^(∘).

Subchapter links

Try It p.112-113

Self-Assessment for Concepts & Skills p.113

Self-Assessment for Problem Solving p.114

Review & Refresh p.115

Concepts, Skills, & Problem Solving p.115-116