Question

find each missing angle measure.

1. (65x - 12)° (43x + 10)°

Explanation:

Step1: Set up equation using vertical - angle property

Vertical angles are equal. So, $65x - 12=43x + 10$.

Step2: Solve for $x$

Subtract $43x$ from both sides: $65x-43x - 12=43x-43x + 10$, which simplifies to $22x-12 = 10$. Then add 12 to both sides: $22x-12 + 12=10 + 12$, getting $22x=22$. Divide both sides by 22: $x = 1$.

Step3: Find the angle measure

Substitute $x = 1$ into either of the angle - expressions. Using $43x + 10$, we have $43\times1+10=43 + 10=53^{\circ}$. Since vertical angles are equal, both angles measure $53^{\circ}$.

Answer:

$53^{\circ}$