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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 53 Page 343

Draw a diagram and mark the exterior and interior angles.

100^(∘), 115^(∘), 145^(∘)

Practice makes perfect

Let's label all interior and exterior angles of the triangle and put the given measures on the diagram.

We will find the exterior angle measures one at a time.

Finding m∠ 4

Notice that angles ∠ 1 and ∠ 2 together form a straight angle, so their measures add to 180^(∘).

Since the measure of ∠ 1 is given, this allows us to set up and solve an equation for m∠ 4.

m∠ 1+m∠ 4=180

m∠ 1= 35

35+m∠ 4=180

LHS-35=RHS-35

m∠ 4=145

Finding m∠ 5

We can similarly find the measure of ∠ 5.

m∠ 2+m∠ 5=180

m∠ 2= 80

80+m∠ 5=180

LHS-80=RHS-80

m∠ 5=100

Finding m∠ 6

Since the measure of the interior angle adjacent to ∠ 6 is not given, we use a different approach to find its measure. Notice that the measures of the two remote interior angles are given.

The Exterior Angle Theorem tells us about the relationship between these angles. This allows us to find the measure of ∠ 6.

m∠ 6=m∠ 1+m∠ 2

m∠ 1= 35, m∠ 2= 80

m∠ 6= 35+ 80

Add terms

m∠ 6=115

Summary

The diagram below shows all exterior angle measures of the triangle.

Subchapter links

Exercises p.339-343