Class 9 Exam > Class 9 Questions > If the arms of one angle are respectively par...
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If the arms of one angle are respectively parallel to the arms of another angle, then the two angles are :
- a)Neither equal nor supplementary
- b)Not equal but supplementary
- c)Equal but not supplementary
- d)Either equal or supplementary
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If the arms of one angle are respectively parallel to the arms of anot...
Explanation:
Let's consider two angles, say angle A and angle B, whose arms are respectively parallel to the arms of another angle, say angle C.
Case 1: The arms of angles A and C are parallel to the arms of angle B
In this case, we can say that angle A and angle B are alternate interior angles. According to the alternate interior angles theorem, alternate interior angles formed by a transversal and two parallel lines are equal. Therefore, angle A and angle B are equal.
Also, since angle A and angle B are adjacent angles (they share a common vertex and a common arm), the sum of these angles is equal to the measure of angle C. Therefore, angle A and angle B are supplementary to each other.
So, in this case, we can say that the two angles are both equal and supplementary.
Case 2: The arms of angles A and B are parallel to the arms of angle C
In this case, we can say that angle C and angle B are corresponding angles. According to the corresponding angles theorem, corresponding angles formed by a transversal and two parallel lines are equal. Therefore, angle C and angle B are equal.
Also, since angle A and angle B are adjacent angles (they share a common vertex and a common arm), the sum of these angles is equal to the measure of angle C. Therefore, angle A and angle B are supplementary to each other.
So, in this case, we can say that the two angles are both equal and supplementary.
Conclusion
Thus, we can conclude that if the arms of one angle are respectively parallel to the arms of another angle, then the two angles are either equal or supplementary.
Therefore, the correct answer is option D - Either equal or supplementary.
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Community Answer
If the arms of one angle are respectively parallel to the arms of anot...
- Option A: "Neither equal nor supplementary"
This is incorrect because the angles will either be equal or supplementary. - Option B: "Not equal but supplementary"
This is partially correct but does not include the case when the angles are equal. - Option C: "Equal but not supplementary"
This is also partially correct but does not include the case when the angles are supplementary. - Option D: "Either equal or supplementary"
This is correct as it covers both possibilities.
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If the arms of one angle are respectively parallel to the arms of another angle, then the two angles are :a)Neither equal nor supplementaryb)Not equal but supplementaryc)Equal but not supplementaryd)Either equal or supplementaryCorrect answer is option 'D'. Can you explain this answer?
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