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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

1. Angles of Triangles

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Exercise 26 Page 340

Focus on the leftmost triangle in the figure.

26^(∘)

Practice makes perfect

Let's highlight ∠ 3, which we are asked to find. We will focus on the triangle that has it as one of its angles. Notice that the measure of one interior and exterior angle of this triangle is given on the figure.

The Exterior Angle Theorem tells about a relationship between these angles.

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

This theorem lets us set up and solve an equation for m∠ 3. 25^(∘) +m∠ 3=51^(∘) → m∠ 3 =26^(∘)

Extra

The Interior and Exterior of an Angle

Recall that an angle divides the plane into two parts:

the region between the sides, or interior of the angle, and
the region outside the sides, or exterior of the angle.

These regions can be examined in the following graph.

Notice that the interior of an angle is the region for which the angle measure is less than 180^(∘).

Subchapter links

Exercises p.339-343