Question

Which of the given statements are correct when two straight lines intersect?
Adjacent angles are complementary
Adjacent angles are supplementary
Opposite angles are equal
Opposite angles are supplementary
A. (i) and (ii) only
B. (ii) and (iii) only
C. (i) and (iv) only
D. (ii) and (iv) only

Answer 1

Hint:
This is a statement based, Hence we will look into each statement and select or eliminate the ones which are true or false. In this question, linear pair property and the property of vertically opposite angles are used to select or eliminate the statement. Then we would compare our answer to the options given and choose the option which would contain correct statements according to us.

Complete step by step solution:
We know that according to the linear pair property of two lines intersecting,

The sum of the adjacent angles is always equal to $180^\circ $ … (1)

We know that a supplementary pair is the pair of any two angles whose sum results in $180^\circ $ … (2)

We know that a complementary pair is the pair of any two angles whose sum results in $90^\circ $ … (3)

By using (1),(2), and (3), we can say that
Adjacent angles are supplementary
Hence, statement (ii) is true, therefore selected

Also, since The sum of the adjacent angles can never be equal to $90^\circ $ ,
So, statement (i) is false, Hence eliminated.

We know that according to the vertically opposite angles property of two lines intersecting,

The pair of vertically opposite angles are always equal to each other … (4)

According to (4), we can easily say that in two straight lines intersecting,
Opposite angles are equal
Hence, statement (iii) is true, therefore selected

For statement (iv), it is only true when the vertically opposite angles are equal to $90^\circ $, but for all other cases, it is false.
So, statement (iv) is false, Hence eliminated.

Since statements (ii) and (iii), are the correct ones,

Hence, B is the final answer.

Note:
These are some very basic statements regarding the concept of two straight lines intersecting, it is advisable to memorize the correct statements as they are also used to solve some high-level questions with ease, also if we would have memorized the correct statements beforehand, we would have easily predicted the correct answer just by looking at the question.