Question

(24x - 2)° y (25x - 8)°

Explanation:

Step1: Identify angle - relationship

The two angles $(24x - 2)^{\circ}$ and $(25x - 8)^{\circ}$ are vertical angles. Vertical angles are equal. So we set up the equation $24x-2 = 25x - 8$.

Step2: Solve the equation for x

Subtract $24x$ from both sides: $-2=x - 8$. Then add 8 to both sides: $x=6$.

Step3: Find the value of one of the angles

Substitute $x = 6$ into $(24x - 2)^{\circ}$. We get $24\times6-2=144 - 2=142^{\circ}$.

Step4: Find the value of y

Since $y$ and $(24x - 2)^{\circ}$ are supplementary (linear - pair, sum to $180^{\circ}$), then $y=180-(24x - 2)$. Substitute $x = 6$: $y=180 - 142=38^{\circ}$.

Answer:

$x = 6$, $y=38^{\circ}$