Question

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.

• A. (i) and (iii)
• B. (ii) and (iii)
• C. (i) and (iv)
• D. (ii) and (iv)

Answer 1

The correct option is B (ii) and (iii)

Let us draw the diagram showing two straight lines $AB$ and $CD$ intersecting each other at point $O.$

$\left(i\right)$ When two lines intersect adjacent angles are complementary.

This statement is incorrect.

As the adjacent angles form a linear pair and they are supplementary.

$\left(ii\right)$ When two lines intersect adjacent angles are supplementary.

This statement is correct.

As the adjacent angles form a linear pair and they are supplementary.

$\left(iii\right)$ When two lines intersect opposite angles are equal.

This statement is correct.

As the vertically opposite angles are equal.

$\left(iv\right)$ When two lines intersect opposite angles are supplementary.

This statement is incorrect.

As the vertically opposite angles are equal.

$\therefore$ Statement $\left(ii\right)$ and $\left(iii\right)$ are correct.