Question

find the measure of ∠mon. m∠mon =

Explanation:

Step1: Set up equation using vertical - angle property

Vertical angles are equal. So, $12x + 30=9x + 48$.

Step2: Solve for x

Subtract $9x$ from both sides: $12x-9x + 30=9x-9x + 48$, which simplifies to $3x+30 = 48$. Then subtract 30 from both sides: $3x+30 - 30=48 - 30$, getting $3x=18$. Divide both sides by 3: $x = 6$.

Step3: Find the measure of $\angle MON$

Substitute $x = 6$ into the expression for $\angle MON$ (either $12x + 30$ or $9x + 48$). Using $9x + 48$, we have $9\times6+48=54 + 48=102$.

Answer:

$102$