Question

53° 127° 3x - 5 y date: 10/9/25

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. The angle with measure $53^{\circ}$ and the angle with measure $y$ are vertical angles. So $y = 53^{\circ}$.

Step2: Set up an equation for the other pair of vertical angles

The angle with measure $127^{\circ}$ and the angle with measure $3x - 5$ are vertical angles, so $3x-5=127$.

Step3: Solve the equation for $x$

Add 5 to both sides of the equation: $3x=127 + 5=132$. Then divide both sides by 3: $x=\frac{132}{3}=44$.

Answer:

$x = 44$, $y = 53$