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Big Ideas Math Geometry, 2014

BI

Big Ideas Math Geometry, 2014 View details

6. Describing Pairs of Angles

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Exercise 12 Page 52

The two angles are complementary angles.

m∠ BAC=58^(∘)
m∠ DAC=32^(∘)

Practice makes perfect

Let's begin by labeling the two angles.

Since ∠ BAC and ∠ DAC are complementary angles, we know that the sum of their measures should equal 90^(∘). We can solve for x by creating an equation using the expressions for the two smaller angles and their sum.

m∠ BAC+m∠ DAC=90

m∠ BAC= 15x-2, m∠ DAC= 7x+4

( 15x-2)+( 7x+4)=90

Remove parentheses

15x-2+7x+4=90

Add and subtract terms

22x+2=90

LHS-2=RHS-2

22x=88

.LHS /22.=.RHS /22.

x= 4

Having solved the equation, we can calculate the individual angles by substituting x= 4 into the expressions for the unknown angles. m∠ BAC ⇒ & 15( 4) - 2 = 58^(∘) m∠ DAC ⇒ & 7( 4) + 4= 32^(∘)

Subchapter links

Communicate Your Answer p.47

Monitoring Progress p.49-51

Exercises p.52-54