Question

Line t intersects parallel lines 1 and 2 as shown below.

According to the information provided, which of the following pairs of angles are not always congruent?

a. same side exterior angles 2 and 7
b.alternate exterior angles 1 and 7
c.corresponding angles 3 and 7
d.vertical angles 5 and 7

Answer 1

Your 14 years old and you don’t know how to do it haha

Answer 2

The correct answer is option d.) vertical angles 5 and 7.

In the given diagram, line
`\( t \)` intersects parallel lines 1 and 2, creating several pairs of angles. Let's analyze each option:

a. Same side exterior angles 2 and 7:

- These angles are always congruent. Same side exterior angles formed by a transversal cutting parallel lines are supplementary, and in this case, angles 2 and 7 are supplementary.

b. Alternate exterior angles 1 and 7:

- These angles are always congruent. Alternate exterior angles formed by a transversal cutting parallel lines are congruent, and in this case, angles 1 and 7 are congruent.

c. Corresponding angles 3 and 7:

- These angles are always congruent. Corresponding angles formed by a transversal cutting parallel lines are congruent, and in this case, angles 3 and 7 are congruent.

d. Vertical angles 5 and 7:

- These angles are not always congruent. Vertical angles formed by intersecting lines are always congruent, but angle 5 is not a vertical angle to angle 7.

The pair of angles that are not always congruent is option d. Vertical angles 5 and 7 are not always congruent.

Therefore, the correct option is d.