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.


ANSWER

(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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