Question

1. $overrightarrow{qs}$ bisects $angle pqr$. what is $mangle pqr$? (hint: solve for $x$ and plug the value back in. dont forget to add the final two angles together.)

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{QS}$ bisects $\angle PQR$, then $m\angle PQS=m\angle SQR$. So, $3x + 5=2x+25$.

Step2: Solve the equation for $x$

Subtract $2x$ from both sides: $3x-2x+5=2x - 2x+25$, which simplifies to $x + 5=25$. Then subtract 5 from both sides: $x=25 - 5=20$.

Step3: Find the measure of $\angle PQS$ and $\angle SQR$

Substitute $x = 20$ into the expression for $\angle PQS$: $m\angle PQS=3x + 5=3\times20+5=60 + 5=65^{\circ}$. Since $m\angle SQR=m\angle PQS$, $m\angle SQR = 65^{\circ}$.

Step4: Calculate $m\angle PQR$

$m\angle PQR=m\angle PQS+m\angle SQR$. So, $m\angle PQR=65^{\circ}+65^{\circ}=130^{\circ}$.

Answer:

$130^{\circ}$