Question

if ∠3 = 5y + 15 and ∠6 = 3y + 45 are alternate interior angles, what is the value of y? a. 20 b. 10 c. 25 d. 15 which angles are supplementary when two parallel lines are intersected by a transversal? a. alternate exterior angles b. alternate interior angles c. corresponding angles d. consecutive interior angles

Explanation:

Step1: Recall property of alternate - interior angles

Alternate - interior angles are equal when two parallel lines are intersected by a transversal. So, $\angle3=\angle6$.

Step2: Set up the equation

Set $5y + 15=3y + 45$.

Step3: Solve the equation for $y$

Subtract $3y$ from both sides: $5y-3y + 15=3y-3y + 45$, which simplifies to $2y+15 = 45$.
Subtract 15 from both sides: $2y+15 - 15=45 - 15$, getting $2y=30$.
Divide both sides by 2: $\frac{2y}{2}=\frac{30}{2}$, so $y = 15$.

For the second question:
Recall angle - relationships when parallel lines are intersected by a transversal. Consecutive interior angles are supplementary.

Answer:

1. d. 15
2. d. Consecutive interior angles