If two lines intersect each other- then the vertically opposite angles - -are complementaryare supplementaryform a linear pairare equal

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Standard IX

Mathematics

Alternate Angles Theorem

If two lines ...

Question

If two lines intersect each other, then the vertically opposite angles _______ .

are complementary

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are supplementary

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form a linear pair

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are equal

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Solution

The correct option is D are equal
If two lines intersect each other, then the vertically opposite angles are equal.

Here, AB and CD intersect at O.
$∠ A O C = ∠ B O D$
$∠ C O B = ∠ A O D$

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Similar questions

Fill in the blanks:

(i) If two angles are complementary, then the sum of their measures is _______.

(ii) If two angles are supplementary, then the sum of their measures is _______.

(iii) Two angles forming a linear pair are _______.

(iv) If two adjacent angles are supplementary, they form a _______.

(v) If two lines intersect at a point, then the vertically opposite angles are always _______.

(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are _______.

Q. Write 'T' for true and 'F' for false

(i) If two parallel lines are cut by a transversal, then the alternate interior angles are equal.
(ii) If two lines intersect each other, then the vertically opposite angles are equal.
(iii) Each acute angle of an isosceles right triangle measures 60°.
(iv) A right triangle cannot have an obtuse angle.

Assertion : If a transversal intersects two lines such that a pair of corresponding angles is equal, then the two lines are parallel to each other.
Reason : If two lines intersect each other, then the vertically opposite angles are equal.
Which of the following is correct

If two lines intersect at a point and if one pair of vertically opposite angles are acute, then the other pair of vertically opposite angles are.

Q. If two lines intersect at a point, then the vertically opposite angles are always equal.

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If two lines intersect each other, then the vertically opposite angles _______ .

The correct option is D are equalIf two lines intersect each other, then the vertically opposite angles are equal. Here, AB and CD intersect at O. ∠AOC=∠BOD ∠COB=∠AOD

The correct option is D are equal
If two lines intersect each other, then the vertically opposite angles are equal.

Here, AB and CD intersect at O.
$∠ A O C = ∠ B O D$
$∠ C O B = ∠ A O D$