Question

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

Explanation:

Step1: Recall angle - bisector property

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

Step2: Substitute given values

We know $m\angle PMN = 74^{\circ}$ and $m\angle OMN=(2x + 7)^{\circ}$. So, $2x+7=\frac{74}{2}$.

Step3: Simplify the right - hand side

$\frac{74}{2}=37$, so the equation becomes $2x + 7=37$.

Step4: Solve for $x$

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

Answer:

$x = 15$