If two straight lines intersect, the measures of the vertically opposite angles are _______.

Equal

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Not equal

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Right angle

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Can't be determined

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Solution

The correct option is A 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.

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Similar questions

Q. If two straight lines intersect, the measures of the vertically opposite angle are .................

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

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(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 _______.

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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.

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