Question

if ∠5 = 4x + 20 and ∠6 = 2x + 40 are alternate exterior angles, what is the value of x?
a. 30
b. 25
c. 15
d. 10
which angles are congruent when two parallel lines are intersected by a transversal?
a. same - side interior angles
b. alternate interior angles
c. supplementary angles

Explanation:

Step1: Recall angle - property

Alternate exterior angles are congruent. So, $\angle5=\angle6$.

Step2: Set up the equation

$4x + 20=2x + 40$.

Step3: Solve for $x$

Subtract $2x$ from both sides: $4x-2x + 20=2x-2x + 40$, which simplifies to $2x+20 = 40$. Then subtract 20 from both sides: $2x+20 - 20=40 - 20$, getting $2x=20$. Divide both sides by 2: $\frac{2x}{2}=\frac{20}{2}$, so $x = 10$.

For the second question:
When two parallel lines are intersected by a transversal, alternate interior angles are congruent.

Answer:

1. d. 10
2. b. Alternate interior angles