Question

1. if $overrightarrow{mo}$ bisects $angle pmn$, $mangle pmn = 74^{circ}$, and $mangle omn = 2x + 7$, find the value of $x$.

Explanation:

Step1: Recall angle - bisector property

Since $\overrightarrow{MO}$ bisects $\angle PMN$, then $m\angle OMN=\frac{1}{2}m\angle PMN$.

Step2: Substitute given values

We know $m\angle PMN = 74^{\circ}$, so $m\angle OMN=\frac{74^{\circ}}{2}=37^{\circ}$.

Step3: Set up an equation

We are given that $m\angle OMN = 2x + 7$. So, $2x+7 = 37$.

Step4: Solve for x

Subtract 7 from both sides: $2x=37 - 7=30$. Then divide both sides by 2: $x=\frac{30}{2}=15$.

Answer:

$x = 15$