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Big Ideas Math: Modeling Real Life, Grade 8

BI

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

Cumulative Practice

Exercise 8 Page 232

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

63^(∘)

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 (2x+1)^(∘) and the measures of the nonadjacent interior angles are x^(∘) and 64^(∘). By the Exterior Angle Measures of a Triangle Theorem, we can write an equation in terms of x. (2x+1)^(∘) = x^(∘) + 64^(∘) Let's solve the equation! For simplicity, we will not write the degree symbol while solving.

2x+1 = x + 64

▼

Solve for x

LHS-x=RHS-x

x + 1 = 64

LHS-1=RHS-1

x = 63

The measure of the exterior angle is 63^(∘).

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