When two straight lines intersect- which of the following statements is-are true- nbsp-Adjacent angles are complementary-Adjacent angles are supplementary-Vertically opposite angles are equal- nbsp-Vertically opposite angles are supplementary-

Byju's Answer

Standard IX

Mathematics

Vertically Opposite Angles

When two stra...

Question

When two straight lines intersect, which of the following statements is/are true?

Adjacent angles are complementary.

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Adjacent angles are supplementary.

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Vertically opposite angles are equal.

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Vertically opposite angles are supplementary.

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Solution

The correct options are
B Adjacent angles are supplementary.
C Vertically opposite angles are equal.

When two straight lines intersect, then the adjacent angles are supplementary and the vertically opposite angles are equal. In the given diagram, two straight lines intersect.
$∠ 1$ and $∠ 3$ are vertically opposite angles and are equal, while $∠ 1$ and $∠ 2$ are adjacent angles and are supplementary.

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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. Consider the following statements:
When two straight lines intersect:

(i) adjacent angles are complementary

(ii) adjacent angles are supplementary

(iii) opposite angles are equal

(iv) opposite angles are supplementary

Of these statements

(a) (i) and (ii) are correct

(b) (ii) and (iii) are correct

(c) (i) and (iv) are correct

(d) (ii) and (iv) are correct

In the adjoining figure, name the following pairs of angles.

(i) Obtuse vertically opposite angles

(ii) Adjacent complementary angles

(iii) Equal supplementary angles

(iv) Unequal supplementary angles

(v) Adjacent angles that do not form a linear pair

Q. Construct the following figures.
(i) A pair of adjacent angles
(ii) Two supplementary angles which are not adjacent angles.
(iii) A pair of adjacent complementary angles.

In the adjoining figure:

(i) Is ∠1 adjacent to ∠2?

(ii) Is ∠AOC adjacent to ∠AOE?

(iii) Do ∠COE and ∠EOD form a linear pair?

(iv) Are ∠BOD and ∠DOA supplementary?

(v) Is ∠1 vertically opposite to ∠4?

(vi) What is the vertically opposite angle of ∠5?