A transversal intersecting two lines creates eight different angles:

[tex]\[\quad\][/tex] alternate interior angles, and [tex]\[\quad\][/tex] pairs of alternate exterior angles.

A. [tex]$2 \ldots 2 \ldots 2$[/tex]
B. [tex]$4 \ldots 2 \ldots 2$[/tex]
C. [tex]$2 \ldots 2 \ldots 4$[/tex]
D. [tex]$4 \ldots 4 \ldots 4$[/tex]

Please select the best answer from the choices provided:
A
B
C
D

Question

23-06-2024
Mathematics

Answered

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A transversal intersecting two lines creates eight different angles:

[tex]\[\quad\][/tex] alternate interior angles, and [tex]\[\quad\][/tex] pairs of alternate exterior angles.

A. [tex]$2 \ldots 2 \ldots 2$[/tex]
B. [tex]$4 \ldots 2 \ldots 2$[/tex]
C. [tex]$2 \ldots 2 \ldots 4$[/tex]
D. [tex]$4 \ldots 4 \ldots 4$[/tex]

Please select the best answer from the choices provided:
A
B
C
D

Sagot :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-06-23T18:13:38-04:00

To solve this problem, let's first break down the different types of angles created when a transversal intersects two lines.

1. Alternate Interior Angles:
- When a transversal intersects two lines, it creates pairs of angles on the inner side of each line but on opposite sides of the transversal. Since we are dealing with two lines, there will be two pairs (4 individual) of alternate interior angles.

2. Alternate Exterior Angles:
- These are pairs of angles on the outer side of the two lines but on opposite sides of the transversal. As with alternate interior angles, there will be two pairs (4 individual) of alternate exterior angles for two lines.

So, the total count is:
- There are 2 pairs of alternate interior angles.
- There are 4 individual alternate interior angles.
- There are 2 pairs of alternate exterior angles.
- There are 4 individual alternate exterior angles.

Given these, let’s look at the options provided:
- Option A: 2 … 2 … 2
- Option B: 4 … 2 … 2
- Option C: 2 … 2 … 4
- Option D: 4 … 4 … 4

Option D: 4 … 4 … 4 is the correct choice as it correctly reflects the 4 individual alternate interior and alternate exterior angles.

Thus, the best answer is:
D

Sagot :

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