Question

if ∠3 = 5y + 15 and ∠6 = 3y + 45 are alternate interior angles, what is the value of y?
a. 10
b. 25
c. 15
d. 20

Explanation:

Step1: Set the angles equal

Since alternate - interior angles are equal, we set $\angle3=\angle6$. So, $5y + 15=3y + 45$.

Step2: Subtract $3y$ from both sides

$5y-3y + 15=3y-3y + 45$, which simplifies to $2y+15 = 45$.

Step3: Subtract 15 from both sides

$2y+15 - 15=45 - 15$, resulting in $2y=30$.

Step4: Divide both sides by 2

$\frac{2y}{2}=\frac{30}{2}$, so $y = 15$.

Answer:

C. 15