Question

find the measure of angle 1.

Explanation:

Step1: Use the property of parallel lines

Since the two lines are parallel, the corresponding angles are equal. So, $8x - 4=6x + 8$.

Step2: Solve the equation for $x$

Subtract $6x$ from both sides: $8x-6x - 4=6x-6x + 8$, which simplifies to $2x-4 = 8$.
Add $4$ to both sides: $2x-4 + 4=8 + 4$, so $2x=12$.
Divide both sides by $2$: $x = 6$.

Step3: Find the measure of the angle

Substitute $x = 6$ into $6x + 8$: $6\times6+8=36 + 8=44$.
Angle $1$ and the angle $6x + 8$ are vertical angles. Vertical angles are equal. So the measure of angle $1$ is $44^{\circ}$.

Answer:

$44^{\circ}$