Mathematics

# 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.

(ii) and (iii)

##### SOLUTION

Let us draw the diagram showing two straight lines $AB$ and $CD$ intersecting each other at point $O.$
$(i)$ When two lines intersect adjacent angles are complementary.
This statement is incorrect.
As the adjacent angles form a linear pair and they are supplementary.

$(ii)$ When two lines intersect adjacent angles are supplementary.
This statement is correct.
As the adjacent angles form a linear pair and they are supplementary.

$(iii)$  When two lines intersect opposite angles are equal.
This statement is correct.
As the vertically opposite angles are equal.

$(iv)$ When two lines intersect opposite angles are supplementary.
This statement is incorrect.
As the vertically opposite angles are equal.
$\therefore$  Statement $(ii)$ and $(iii)$ are correct.

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Single Correct Medium Published on 09th 09, 2020
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