Question

Consider the following statements: When two straight lines intersect, then:
[I.] Adjacent angles are complementary
[II.] Adjacent angles are supplementary
[III.] Opposite angles are equal
[IV.] Opposite angles are supplementary Which of these statements are correct?

• A. I and III are correct
• B. II and III are correct
• C. I and IV are correct
• D. II and IV are correct

Hint:

At an intersection, vertically opposite angles are equal and adjacent angles are supplementary (sum to 180°), not complementary.

Answer 1

The Correct Option is B

Let us examine each statement:
[I.] False — Adjacent angles at an intersection are not necessarily complementary (sum is not always 90°).
[II.] True — Adjacent angles formed at a point of intersection sum up to 180°, so they are supplementary.
[III.] True — Vertically opposite angles formed by intersecting lines are always equal.
[IV.] False — Opposite angles are equal, but not necessarily supplementary unless each is 90°, which is not always the case. Therefore, only (II) and (III) are correct.
\[ {\text{Statements II and III are correct}} \]