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

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

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

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Solution

Let us draw the following diagram showing two straight lines AD and BC intersecting each other at a point.

Now, let us consider each statement one by one:

(i)

When two lines intersect adjacent angles are complementary.

This statement is __incorrect__

Explanation:

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.__

Explanation:

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.__

Explanation:

As the vertically opposite angles are equal.

(iv) When two lines intersect opposite angles are supplementary.

This statement is __incorrect.__

Explanation:

As the vertically opposite angles are equal

Thus, out of all, (ii) and (iii) are correct.

Hence, the correct choice is (b).

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