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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 11 Page 52

The two angles are supplementary.

m∠ QRT=47^(∘)
m∠ SRT=133^(∘)

Practice makes perfect

Let's begin by labeling the two angles.

Since ∠ QRT and ∠ SRT are supplementary angles, we know that the sum of their measures should equal 180^(∘). We can solve for x by creating an equation using the expressions for the two smaller angles and their sum.

m∠ QRT+m∠ SRT=180

m∠ QRT= 3x+5, m∠ SRT= 10x-7

( 3x+5)+( 10x-7)=180

Remove parentheses

3x+5+10x-7=180

Add and subtract terms

13x-2=180

LHS+2=RHS+2

13x=182

.LHS /13.=.RHS /13.

x= 14

Having solved the equation, we can calculate the individual angles by substituting x= 14 into the expressions for the unknown angles. m∠ QRT ⇒ & 3( 14) + 5 = 47^(∘) m∠ SRT ⇒ & 10( 14) - 7 = 133^(∘)

Subchapter links

Communicate Your Answer p.47

Monitoring Progress p.49-51

Exercises p.52-54