Question

if m bisects ∠pmn, m∠pmo = 73°, and m∠omn = 3x + 7, then what is the measure of each angle?
x=
m∠omn=
m∠pmn=

Explanation:

Step1: Set up equation

Since $\angle PMO$ and $\angle OMN$ are supplementary (assuming they form a straight - line angle and $\angle PMN$ is a straight - line angle, so $\angle PMO+\angle OMN = 180^{\circ}$), we have the equation $73+(3x + 7)=180$.

Step2: Simplify the left - hand side

Combine like terms: $73+3x + 7=3x+80$. So the equation becomes $3x + 80=180$.

Step3: Solve for $x$

Subtract 80 from both sides: $3x=180 - 80=100$. Then divide both sides by 3: $x=\frac{100}{3}$.

Step4: Find $\angle OMN$

Substitute $x = \frac{100}{3}$ into the expression for $\angle OMN$: $\angle OMN=3x + 7=3\times\frac{100}{3}+7=100 + 7=107^{\circ}$.

Step5: Find $\angle PMN$

Since $\angle PMN$ is a straight - line angle, $\angle PMN = 180^{\circ}$.

Answer:

$x=\frac{100}{3}$
$m\angle OMN = 107^{\circ}$
$m\angle PMN = 180^{\circ}$