Consider the following statements:
When two straight lines intersect:
(i) 0Adjacent angles are complementary
(ii) Adjacent angles are supplementary.
(iii) Opposite angles are equal.
(iv) Opposite angles are supplementary.
Of these statements
A. (i) and (iii) are correct
B. (ii) and (iii) are correct
C. (i) and (iv) are correct
D. (ii) and (iv) are correct
Answers
When two straight lines intersect, the adjacent angles are supplementary, and opposite angles are equal. Hence, option (B) is correct.
(i) Adjacent angles are complementary when two lines intersect. This statement is false.
• Adjacent angles are called complementary if their sum is equal to 90°.
• However, from the image attached, we can see that the angles do not sum up to 90° when two straight lines intersect.
• Therefore, the adjacent angles are not complementary.
(ii) When two lines intersect, the adjacent angles are supplementary. This statement is true.
• Adjacent angles are said to be supplementary if their degrees of angle sum up to 180°.
• When any two lines intersect, the adjacent angles together form a straight line, and a straight line always has an angle of 180°.
• Therefore, the sum of two adjacent angles in the image attached below is 180°, and are supplementary to each other.
(iii) When two lines intersect each other, opposite angles are equal. This statement is true because when two lines intersect each other, the angles sharing a common vertex and lying opposite to each other are equal in degrees.
(iv) When two lines intersect, the opposite angles are supplementary. This statement is false, because a supplementary angle (180°) is formed on a straight line, and the opposite angles formed on intersection of two lines never lie in a straight line.
• Therefore, only statements (ii) and (iii) are correct. Hence, option (B) is the right answer.
Answer:
option B is correct amswer