Question

if ∠2 = 3z + 45 and ∠6 = 5z - 15 are alternate interior angles, find z.
a. 25
b. 10
c. 30
d. 20

Explanation:

Step1: Set the angles equal

Since alternate - interior angles are equal, we set $3z + 45=5z - 15$.

Step2: Move z terms to one side

Subtract $3z$ from both sides: $45 = 5z-3z - 15$, which simplifies to $45 = 2z-15$.

Step3: Isolate the variable term

Add 15 to both sides: $45 + 15=2z$, so $60 = 2z$.

Step4: Solve for z

Divide both sides by 2: $z=\frac{60}{2}=30$.

Answer:

D. 20