Question

1. in the diagram shown, mo bisects ∠nmp. if m∠nmp = 74° and m∠nmo = 4(x + 2), then find the value of x. do not round.

Explanation:

Step1: Recall angle - bisector property

An angle - bisector divides an angle into two equal angles. So, if $MO$ bisects $\angle NMP$, then $m\angle NMO=\frac{1}{2}m\angle NMP$.
Given $m\angle NMP = 74^{\circ}$, then $m\angle NMO=\frac{74}{2}=37^{\circ}$.

Step2: Set up an equation

We are given that $m\angle NMO = 4(x + 2)$. Since $m\angle NMO=37^{\circ}$, we set up the equation $4(x + 2)=37$.

Step3: Expand the left - hand side

Using the distributive property $a(b + c)=ab+ac$, we have $4x+8 = 37$.

Step4: Solve for $x$

Subtract 8 from both sides of the equation: $4x=37 - 8$, so $4x=29$.
Then divide both sides by 4: $x=\frac{29}{4}=7.25$.

Answer:

$x = 7.25$