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Consider the following statements
If two straight lines intersect, then
I. vertically opposite angles are equal.
II. vertically opposite angles are supplementary.
III. adjacent angles are complementary.
I. vertically opposite angles are equal.
II. vertically opposite angles are supplementary.
III. adjacent angles are complementary.
Which of the statements given above is/are correct?
- a)Only III
- b)Only I
- c)II and III
- d)II and II
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Consider the following statementsIf two straight lines intersect, then...
Here, AB and CD are two lines.
If two straight lines intersect, then opposite vertically angles are equal.
Hence, option B is correct.
If two straight lines intersect, then opposite vertically angles are equal.
Hence, option B is correct.
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Community Answer
Consider the following statementsIf two straight lines intersect, then...
Explanation:
To determine which of the given statements are correct, let's examine each statement individually:
I. Vertically opposite angles are equal:
- Vertically opposite angles are formed when two lines intersect. These angles are opposite each other and are formed by the intersection of the lines.
- By the nature of intersecting lines, vertically opposite angles are always equal. This means that if two lines intersect, the vertically opposite angles will have the same measure.
- Therefore, Statement I is correct.
II. Vertically opposite angles are supplementary:
- This statement is incorrect.
- By definition, supplementary angles are angles that add up to 180 degrees. Vertically opposite angles are equal, but they do not add up to 180 degrees.
- Therefore, Statement II is incorrect.
III. Adjacent angles are complementary:
- This statement is incorrect.
- By definition, complementary angles are angles that add up to 90 degrees. Adjacent angles are angles that share a common vertex and a common side, but they do not necessarily add up to 90 degrees.
- Therefore, Statement III is incorrect.
Therefore, the correct statement is only Statement I: Vertically opposite angles are equal.
Summary:
- Statement I is correct: Vertically opposite angles are equal.
- Statement II is incorrect: Vertically opposite angles are not supplementary.
- Statement III is incorrect: Adjacent angles are not necessarily complementary.
To determine which of the given statements are correct, let's examine each statement individually:
I. Vertically opposite angles are equal:
- Vertically opposite angles are formed when two lines intersect. These angles are opposite each other and are formed by the intersection of the lines.
- By the nature of intersecting lines, vertically opposite angles are always equal. This means that if two lines intersect, the vertically opposite angles will have the same measure.
- Therefore, Statement I is correct.
II. Vertically opposite angles are supplementary:
- This statement is incorrect.
- By definition, supplementary angles are angles that add up to 180 degrees. Vertically opposite angles are equal, but they do not add up to 180 degrees.
- Therefore, Statement II is incorrect.
III. Adjacent angles are complementary:
- This statement is incorrect.
- By definition, complementary angles are angles that add up to 90 degrees. Adjacent angles are angles that share a common vertex and a common side, but they do not necessarily add up to 90 degrees.
- Therefore, Statement III is incorrect.
Therefore, the correct statement is only Statement I: Vertically opposite angles are equal.
Summary:
- Statement I is correct: Vertically opposite angles are equal.
- Statement II is incorrect: Vertically opposite angles are not supplementary.
- Statement III is incorrect: Adjacent angles are not necessarily complementary.
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Consider the following statementsIf two straight lines intersect, thenI. vertically opposite angles are equal.II. vertically opposite angles are supplementary.III. adjacent angles are complementary.Which of the statements given above is/are correct?a)Only IIIb)Only Ic)II and IIId)II and IICorrect answer is option 'B'. Can you explain this answer?
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