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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

6. Describing Pairs of Angles

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Exercise 40 Page 429

If you have an acute angle, what is the measure of its complement and its supplement?

Never

Practice makes perfect

An acute angle is an angle that is between 0^(∘) and 90^(∘). Let's draw an arbitrary ∠ A that fits this description.

The sum of ∠ A and its complement equals a right angle, while the sum of ∠ A and its supplement equals a straight angle.

With the information in the diagram, we can write two separate equations. & m∠ A+ m∠ B=90^(∘) & m∠ A+m∠ C=180^(∘) Let's solve these equations for m∠ A. & m∠ A=90^(∘) - m∠ B & m∠ A=180^(∘) -m∠ C Now that we have two equation that describe m∠ A in terms of m∠ B and m∠ C, we can write a new relation that is between m∠ B and m∠ C.

m∠ A = 90^(∘) -m∠ B

m∠ A = 180^(∘) -m∠ C

180^(∘) -m∠ C= 90^(∘) -m∠ B

▼

Solve for m∠ C

LHS-180^(∘)=RHS-180^(∘)

- m∠ C= -90^(∘) -m∠ B

LHS * (-1)=RHS* (-1)

m∠ C= 90^(∘) +m∠ B

CommutativePropAdd

Commutative Property of Addition

m∠ C= m∠ B+90^(∘)

As we can see, to obtain m∠ C we have to add 90^(∘) to m∠ B. This must mean that the complement of an angle is never greater than its supplement. m∠ C> m∠ B

Subchapter links

Communicate Your Answer p.423

Monitoring Progress p.425-427

Exercises p.428-430