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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

5. Measuring and Constructing Angles

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Exercise 34 Page 421

When an angle is bisected, it is cut exactly in half.

m∠ PQS=71^(∘)
m∠ PQR=142^(∘)

Practice makes perfect

The expression m∠ PQS indicates the measure of the angle between rays QP and QS. Similarly, the expression m∠ PQR indicates the measure of the angle between rays QP and QR. We are also told that QS bisects ∠ PQR. This means that it cuts the angle exactly in half.

Looking at the figures, we can see that m∠ PQR is equal to the sum of m∠ PQS and m∠ RQS. We can form an equation to solve for the missing angles using the given measure and the fact that the two angles created by the bisector are equal to one another.

m∠ PQS+m∠ RQS=m∠ PQR

m∠ PQS= m∠ RQS

m∠ RQS+m∠ RQS=m∠ PQR

m∠ RQS= 71

71+ 71=m∠ PQR

Add terms

142=m∠ PQR

Rearrange equation

m∠ PQR=142

Finally, let's summarize what we found. m∠ PQS&=71^(∘) m∠ PQR&=142^(∘)

Subchapter links

Communicate Your Answer p.413

Monitoring Progress p.414-418

Exercises p.419-422