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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
1. Angles of Triangles
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Exercise 11 Page 339

Look at the interior angles of the large triangle.

151^(∘)

Practice makes perfect

We are given the measures of two interior angles of a triangle.

We are asked to find the measure of angle 2. To do so, notice that ∠ 5 and ∠ 2 form a linear pair.

We know that angles in a linear pair are supplementary, so their measures add up to 180. Since we know that m∠ 5= 29^(∘), this lets us find m∠ 2.
m∠ 5+m∠ 2=180^(∘)
Substitute

m∠ 5= 29^(∘)

29^(∘)+m∠ 2=180^(∘)
SubEqn

LHS-29^(∘)=RHS-29^(∘)

m∠ 2=151^(∘)
The measure of ∠ 2 is 151^(∘).

Extra

 Pair of Angles

Pairs of angles can be classified in different ways depending on how their measures relate. Let's see this classification in the following table!

Pair of Angles
Complementary Angles Two angles whose measures add up to 90^(∘) or π2 radians.
Supplementary Angles Two angles whose measures add up to 180^(∘) or π radians. They are also called linear pairs because they form a straight angle.
Vertical Angles Vertical angles are formed on opposite sides of the point of intersection.

More information about theorems related to angles can be found on the following pages.

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arrow_right Exercises p.339-343
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