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McGraw Hill Integrated II, 2012 View details

1. Angles of Triangles

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Exercise 6 Page 339

Look for interior and exterior angles.

127^(∘)

Practice makes perfect

Consider the given diagram that represents the triangle formed by the brace and the rest of the frame of a deck chair.

We want to find the measure of angle 6. To do so, notice that angles ∠ 3 and ∠ 6 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∠ 3= 53^(∘), we can use this to find m∠ 6.

m∠ 3+m∠ 6=180^(∘)

Substitute

m∠ 3= 53^(∘)

53^(∘)+m∠ 6=180^(∘)

SubEqn

LHS-53^(∘)=RHS-53^(∘)

m∠ 6=127^(∘)

The measure of ∠ 6 is 127 ^(∘).

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.

Vertical Angles Theorem
Triangle Exterior Angle Theorem
Third Angle Theorem

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Exercises p.339-343

Exercise 6 Page 339

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