Question

if ∠7 = 4b + 25 and ∠2 = 145° are alternate exterior angles, what is the value of b? a. 20 b. 15 c. 25 d. 30 when a transversal intersects two parallel lines, how many angles are formed? a. 10 b. 4 c. 6

Explanation:

Step1: Recall alternate - exterior angles property

Alternate exterior angles are equal when a transversal intersects two parallel lines. So, $\angle7=\angle2$.

Step2: Set up the equation

We have $4b + 25=145$.

Step3: Solve for $b$

Subtract 25 from both sides: $4b=145 - 25=120$. Then divide both sides by 4: $b=\frac{120}{4}=30$.

For the second question:
When a transversal intersects two parallel lines, 8 angles are formed. Each of the two parallel lines is intersected by the transversal at a point, and at each intersection, 4 angles are formed. So in total, $4 + 4=8$ angles are formed.

Answer:

1. A. 20
2. None of the above options are correct. The correct answer is 8.