Question

1. find the value of x if qs bisects ∠pqr and m∠pqr = 82°.

Explanation:

Step1: Recall angle - bisector property

If $\overline{QS}$ bisects $\angle PQR$, then $m\angle PQS=\frac{1}{2}m\angle PQR$.

Step2: Set up the equation

We know that $m\angle PQR = 82^{\circ}$ and $m\angle PQS=(10x + 1)^{\circ}$. So, $10x+1=\frac{82}{2}$.

Step3: Simplify the right - hand side

$\frac{82}{2}=41$, so the equation becomes $10x + 1=41$.

Step4: Solve for x

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

Answer:

$x = 4$