Question

1. write and use an equation to find the value of x that makes the alternate interior angles postulate true. 8x + 12 10x - 10 x =

Explanation:

Step1: Apply alternate - interior angles postulate

According to the alternate - interior angles postulate, when two parallel lines are cut by a transversal, alternate - interior angles are congruent. So, we set up the equation $8x + 12=10x-10$.

Step2: Solve the equation for x

First, subtract $8x$ from both sides:
$8x + 12-8x=10x-10 - 8x$.
This simplifies to $12 = 2x-10$.
Then, add 10 to both sides: $12 + 10=2x-10 + 10$, which gives $22 = 2x$.
Finally, divide both sides by 2: $\frac{22}{2}=\frac{2x}{2}$, so $x = 11$.

Answer:

$11$