When an angle is bisected, it is cut exactly in half.
m∠ RQS=63^(∘)
m∠ PQR=126^(∘)
Practice makes perfect
In this exercise we want to find m∠ RQS and m∠ PQR given that m∠ PQS=63^(∘), and that QS bisects ∠ PQR. This means that it cuts the angle exactly in half. The expression m∠ RQS indicates the measure of the angle between two rays, QR and QS. Similarly, the expression m∠ PQR indicates the measure of the angle between rays QP and QR. Let's identify these angles.
Looking at the figures and from the Angle Addition Postulate, we have 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.
Finally, let's summarize what we found. From the equation we got that m∠ PQR is 126^(∘). Additionally, as we previously stated, the measure of angle ∠ RQS equals the given measure of ∠ PQS. Therefore, m∠ PQS=63^(∘).
m∠ RQS&=63^(∘)
m∠ PQR&=126^(∘)
