NCERT Solutions Class 9 Maths Chapter 6 — Lines & Angles

Solution:

Step 1: The reflex angle of a given angle 'x' is calculated as 360° - x.

Step 2: For an angle of 75°, its reflex angle is 360° - 75° = 285°.

Step 3: An angle that is greater than 180° and less than 360° is classified as a reflex angle.

Solution:

Step 1: Complementary angles are two angles whose sum is 90°.

Step 2: Supplementary angles are two angles whose sum is 180°.

Step 3: A linear pair consists of two adjacent angles that are supplementary, but not all supplementary angles form a linear pair (they don't have to be adjacent).

Solution:

Step 1: The description states that ray QS stands on line PQ, meaning P, Q, S are collinear, and ∠PQS is a straight angle (180°).

Step 2: Angles ∠PQR and ∠RQS are adjacent (they share a common vertex Q and a common arm QR).

Step 3: Since their non-common arms (QP and QS) form a straight line, their sum is 180°.

Step 4: Adjacent angles whose sum is 180° form a linear pair.

Solution:

Step 1: When two lines intersect, they form two pairs of vertically opposite angles.

Step 2: A key theorem states that vertically opposite angles are always equal.

Step 3: Therefore, if one angle is 65°, its vertically opposite angle must also be 65°.

Solution:

Step 1: When lines AB and CD intersect at O, angles ∠AOC and ∠BOC are adjacent angles.

Step 2: They form a linear pair along the line AB (or CD, depending on how they are viewed, but specifically on line AB).

Step 3: According to the linear pair axiom, the sum of angles in a linear pair is 180°, not 90°.

Step 4: Concluding their sum is 90° implies they are complementary, which is incorrect for a linear pair unless one of them is 0° and the other 90°, which is not the general case.