If two lines intersect each other, then the vertically opposite angles are ……….a)Equalb)Supplementaryc)Unequald)ComplementaryCorrect answer is option 'A'. Can you explain this answer?

Question

If two lines intersect each other, then the vertically opposite angles are &#8230;&#8230;&#8230;.a)Equalb)Supplementaryc)Unequald)ComplementaryCorrect answer is option 'A'. Can you explain this answer?

Answer

If two straight lines intersect each other at any point then the angle which are vetically opposite are equal.

Answer

Eqel

Answer

Because when interested two lines each other, then vertically opposite angel are equal

Answer

Equal

Answer

Vertically Opposite Angles

Vertically opposite angles are formed when two lines intersect each other. These angles are opposite to each other and share a common vertex. In other words, they are formed by two intersecting lines and are located opposite to each other.

Equal Angles

When two lines intersect, the vertically opposite angles formed are always equal in measure. This means that if one angle measures x degrees, then the other angle will also measure x degrees. In mathematical terms, if angle A and angle B are vertically opposite angles, then angle A = angle B.

Proof of Equality

To prove that vertically opposite angles are equal, we can use the property of alternate angles or corresponding angles. When two lines intersect, they form four pairs of alternate angles and four pairs of corresponding angles. Alternate angles are equal, and corresponding angles are equal if the lines are parallel.

When two lines intersect, they form two pairs of vertically opposite angles. Let's consider the angles as angle 1 and angle 2. We can prove their equality as follows:

1. Draw a transversal line that intersects the two lines.
2. Use the property of alternate angles or corresponding angles to show that angle 1 is equal to another angle formed by the transversal.
3. Similarly, show that angle 2 is equal to another angle formed by the transversal.
4. Since both angle 1 and angle 2 are equal to the same angle, they must be equal to each other.

Conclusion

In conclusion, when two lines intersect each other, the vertically opposite angles formed are always equal in measure. This property can be proven using the concept of alternate angles or corresponding angles. Understanding the concept of vertically opposite angles is essential in geometry, as it helps in solving various problems related to angles and lines.

Answer

Angles are equal

Answer

Equal

Answer

Supplementary

Answer

If two straight lines intersect each other at any point then the angle which are vetically opposite are equal.

Given two lines AB and CD intersect each other at the point O.
To prove: ∠1 = ∠3 and ∠2 = ∠4
Proof:
From the figure, ∠1 + ∠2 = 180° [Linear pair] → (1)
∠2 + ∠3 = 180° [Linear pair] → (2)
From (1) and (2), we get
∠1 + ∠2 = ∠2 + ∠3
∴ ∠1 = ∠3
Similarly, we can prove ∠2 = ∠4 also.

Similar Class 9 Doubts

If two lines intersect each other then the vertically opposite angles are equal?

If two straight lines intersect each other then prove that the opposite to the bisector of angle performed by sector the vertically opposite angles?

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Prove that if two lines interest each other than prove that the vertically opposite angle are equal?

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