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Answer :
When a transversal cuts through two parallel lines, several types of angles are formed. Specifically, we are interested in the interior angles on the same side of the transversal.
Here is the step-by-step explanation:
1. Identify the Parallel Lines and the Transversal:
- Let's designate the two parallel lines as Line 1 and Line 2.
- The transversal is the line that intersects both Line 1 and Line 2.
2. Locate the Interior Angles:
- When the transversal intersects the parallel lines, it creates two pairs of interior angles on the same side of the transversal.
- Let's call these angles [tex]\(\angle A\)[/tex] and [tex]\(\angle B\)[/tex] on one side of the transversal.
3. Properties of the Angles:
- According to the properties of parallel lines cut by a transversal, the sum of the interior angles on the same side of the transversal is always 180 degrees. This is because they are supplementary angles.
4. Conclusion:
- Therefore, [tex]\(\angle A + \angle B = 180^\circ\)[/tex].
Thus, the sum of the interior angles on the same side of the transversal is 180 degrees.
Here is the step-by-step explanation:
1. Identify the Parallel Lines and the Transversal:
- Let's designate the two parallel lines as Line 1 and Line 2.
- The transversal is the line that intersects both Line 1 and Line 2.
2. Locate the Interior Angles:
- When the transversal intersects the parallel lines, it creates two pairs of interior angles on the same side of the transversal.
- Let's call these angles [tex]\(\angle A\)[/tex] and [tex]\(\angle B\)[/tex] on one side of the transversal.
3. Properties of the Angles:
- According to the properties of parallel lines cut by a transversal, the sum of the interior angles on the same side of the transversal is always 180 degrees. This is because they are supplementary angles.
4. Conclusion:
- Therefore, [tex]\(\angle A + \angle B = 180^\circ\)[/tex].
Thus, the sum of the interior angles on the same side of the transversal is 180 degrees.
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