Question

find the measure of ∠orq.
(9x - 4)°
(3x + 40)°
m∠orq =

Explanation:

Step1: Set up equation using vertical - angle property

Vertical angles are equal. $\angle MQR$ and $\angle ORP$ are vertical angles. So, $9x - 4=3x + 40$.

Step2: Solve the equation for x

Subtract $3x$ from both sides: $9x-3x - 4=3x-3x + 40$, which simplifies to $6x-4 = 40$. Then add 4 to both sides: $6x-4 + 4=40 + 4$, giving $6x=44$. Divide both sides by 6: $x=\frac{44}{6}=\frac{22}{3}$.

Step3: Find the measure of $\angle ORQ$

$\angle ORQ$ and $\angle ORP$ are supplementary (linear - pair of angles), so $m\angle ORQ=180-(3x + 40)$. Substitute $x = \frac{22}{3}$ into the expression: $3x+40=3\times\frac{22}{3}+40=22 + 40=62$. Then $m\angle ORQ=180 - 62=118$.

Answer:

$118$