Exercise 3 Page 339

80^(∘)

Practice makes perfect

In the provided diagram, we are given the measures of an exterior angle and a remote interior angle of a triangle.

We are asked to find the measure of the other remote interior angle. To do so, we can use the Exterior Angle Theorem.

Exterior Angle Theorem
The measure of an exterior angle is the sum of the measures of the two remote interior angles.

We can use this theorem to set up and solve an equation for m∠ 2. Let's do it! m∠ 2 + 32 ^(∘) = 112 ^(∘) Now we will solve this equation for the measure of angle 2 by subtracting 32 ^(∘) from each side.

32^(∘)+ m∠ 2= 112^(∘)

SubEqn

LHS-32^(∘)=RHS-32^(∘)

m∠ 2=80^(∘)

We have found that the measure of ∠ 2 is 80^(∘).

Extra

Angles of a Triangle

More information about the different relations between the angles in a triangle can be found on the following pages.

Types of Triangles
Interior Angles of a Triangle
Triangle Interior Angle Theorem

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Exercises p.339-343

Exercise 3 Page 339

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