Question

angle r and angle s are vertical angles. if m<r = 2x + 24 and m<s = 144, what is the value of x? 60 84 120 36

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. So, $m\angle R=m\angle S$.

Step2: Set up the equation

Since $m\angle R = 2x + 24$ and $m\angle S=144$, we have the equation $2x + 24=144$.

Step3: Solve for x

Subtract 24 from both sides of the equation: $2x=144 - 24$. So, $2x = 120$. Then divide both sides by 2: $x=\frac{120}{2}=60$.

Answer:

60