Question

1. if qs bisects ∠pqr and m∠pqr = 82°, find each measure. encuentra cada medicion x = m∠pqs = m∠rqs =

Explanation:

Step1: Recall angle - bisector property

Since $\overrightarrow{QS}$ bisects $\angle PQR$, then $m\angle PQS=m\angle RQS=\frac{1}{2}m\angle PQR$.

Step2: Calculate $m\angle PQS$ and $m\angle RQS$

$m\angle PQS = m\angle RQS=\frac{1}{2}\times82^{\circ}=41^{\circ}$.

Step3: Set up an equation for $x$

We know that $m\angle PQS=(10x + 1)^{\circ}$, and $m\angle PQS = 41^{\circ}$. So, $10x+1 = 41$.

Step4: Solve the equation for $x$

Subtract 1 from both sides: $10x=41 - 1=40$. Then divide both sides by 10: $x=\frac{40}{10}=4$.

Answer:

$x = 4$
$m\angle PQS=41^{\circ}$
$m\angle RQS=41^{\circ}$