Question

1. if ∠2 = 3z + 45 and ∠6 = 5z - 15 are alternate interior angles, find z.

a. 30
b. 25
c. 20
d. 10

Explanation:

Step1: Recall property of alternate - interior angles

Alternate - interior angles are equal. So, $\angle2=\angle6$.

Step2: Set up the equation

Set $3z + 45=5z-15$.

Step3: Solve for $z$

First, subtract $3z$ from both sides: $45 = 5z-3z - 15$.
$45=2z - 15$.
Then, add 15 to both sides: $45 + 15=2z$.
$60 = 2z$.
Finally, divide both sides by 2: $z=\frac{60}{2}=30$.

Answer:

a. 30