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Big Ideas Math Integrated I, 2016 View details

5. Measuring and Constructing Angles

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Exercise 35 Page 421

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

m∠ PQS=62^(∘)
m∠ RQS=62^(∘)

Practice makes perfect

The expression m∠ PQS indicates the measure of the angle between rays QP and QS. Similarly, the expression m∠ RQS indicates the measure of the angle between rays QR and QS. 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

Substitute

m∠ RQS= m∠ PQS

m∠ PQS+ m∠ PQS=m∠ PQR

Substitute

m∠ PQR= 124

m∠ PQS+m∠ PQS= 124

AddTerms

Add terms

2m∠ PQS=124

DivEqn

.LHS /2.=.RHS /2.