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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 8 Page 339

Highlight ∠ 5 and the angles with known measure.

131

Practice makes perfect

Let's highlight ∠ 5 and the angles with known measures.

There is no direct connection between angle ∠ 5 and the angles with the given measure. We will find m∠ 5 in two steps.

Step 1: Finding m∠ 2

Let's focus on the part of the diagram around angle ∠ 1. Notice that angles ∠ 1 and ∠ 2 form a linear pair.

We know that angles in a linear pair are supplementary, so their measures add to 180. Since we know that m∠ 1=102, this lets us find m∠ 2.

m∠ 1+m∠ 2=180

m∠ 1= 102

102+m∠ 2=180

LHS-102=RHS-102

m∠ 2=78

The measure of ∠ 2 is 78.

Step 2: Finding m∠ 5

Let's put the measure of ∠ 2 on the diagram and shift our focus to exterior and interior angles of the triangle. Notice that we highlighted an exterior angle and two remote interior angles.

The Exterior Angle Theorem tells 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 relationship lets us set up and solve an equation to find m∠ 5.

m∠ 5=m∠ 2+m∠ 3

m∠ 2= 78, m∠ 3= 53

m∠ 5= 78+ 53

Add terms

m∠ 5=131

The measure of ∠ 5 is 131.

Subchapter links

Exercises p.339-343