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If two lines are intersected by a transv...

If two lines are intersected by a transversal, then the number of pairs of interior angles on the same side of the transversal is

A

1

B

2

C

3

D

4

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to determine the number of pairs of interior angles on the same side of a transversal when it intersects two lines. ### Step-by-Step Solution: 1. **Understand the Concept of Transversal:** A transversal is a line that intersects two or more lines at different points. In this case, we have two lines intersected by one transversal. **Hint:** Visualize the transversal crossing two parallel lines to understand the angles formed. 2. **Identify the Angles Formed:** When a transversal intersects two lines, it creates several angles. Specifically, it creates four interior angles between the two lines. **Hint:** Draw a diagram with two parallel lines and a transversal to see the angles clearly. 3. **Classify the Interior Angles:** The interior angles are those angles that lie between the two lines. For our two lines intersected by the transversal, we can label the angles formed as follows: - Angle 1 (to the left of the transversal on the first line) - Angle 2 (to the right of the transversal on the first line) - Angle 3 (to the left of the transversal on the second line) - Angle 4 (to the right of the transversal on the second line) **Hint:** Remember that interior angles are always located between the two lines. 4. **Identify Pairs of Interior Angles on the Same Side:** We need to find pairs of interior angles that are on the same side of the transversal. - One pair is Angle 1 and Angle 2 (both on the left side of the transversal). - The other pair is Angle 3 and Angle 4 (both on the right side of the transversal). **Hint:** Look for angles that share the same side of the transversal. 5. **Count the Pairs:** From the above identification, we see that there are two pairs of interior angles on the same side of the transversal: - Pair 1: (Angle 1, Angle 2) - Pair 2: (Angle 3, Angle 4) **Hint:** Remember that a pair consists of two angles. 6. **Conclusion:** Therefore, the total number of pairs of interior angles on the same side of the transversal is **2**. ### Final Answer: The number of pairs of interior angles on the same side of the transversal is **2**.
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