Question

If line segments A and B are parallel, which of the following pairs of angles are not equal?

A)
`\angle11` and
`\angle7`
B)
`\angle1` and
`\angle 3`
C)
`\angle6` and
`\angle2`
D)
`\angle3` and
`\angle6`

Answer 1

C: ∠6 and ∠2

Explanation:

Step 1:

∠6 = ∠9 S.S. Int. ∠'s (Same Side Interior ∠'s)

Step 2:

∠9 + ∠2 = 180° Sum of line

Step 3:

∠9 ≠ ∠2

Answer:

C: ∠6 and ∠2

Hope This Helps :)

Answer 2

`\huge\boxed{C}`

Explanation:

Hi there!

A)
`m\angle11, m\angle7`

B)
`m\angle1, m\angle3`

C)
`m\angle6, m\angle2`

D)
`m\angle3, m\angle6`

We need to find which pairs are not equal.

We know that lines a and b are parallel. This means that line c is a transversal, and same with line d.

Let's start with A).

Are
`m\angle11` and
`m\angle7` equal?

Yes. This is true because when c is a transversal, angles 11 and 7 are alternate interior angles, meaning they're congruent, or equal. This is not the correct nswer choice as these angles are equal.

Are
`m\angle1` and
`m\angle3` equal?

Yes. When d is a transversal, angles 1 and 3 are called corresponding angles, which are always equal. Corresponding angles have 1 angle in between them.

Are
`m\angle6` and
`m\angle2` equal?

No. There is no reason that we can use to prove that
`m\angle6` and
`m\angle2` are equal. This means that C is the correct answer.

Are
`m\angle3` and
`m\angle6` equal?

Yes.
`m\angle3` and
`m\angle6` are called vertical angles. They share one vertice, or angle. Vertical angles are always congruent.

The correct answer is:

`\huge\boxed{C}`

Hope this helps :)

Let me know if you have any questions!