When an angle is bisected, it is cut exactly in half.
m∠ PQS=59.5^(∘)
m∠ RQS=59.5^(∘)
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.
