Linear pair of angles are always supplementary. But supplementary angles need not form a linear pair. Why?

1. Angle and its Types:

(i) An angle is the union of two non-collinear rays with a common initial point.

(ii) An angle whose measure is ${90}^{°}$ is called a right angle.

(iii) An angle whose measure is less than ${90}^{°}$ is called an acute angle.

(iv) An angle whose measure is more than ${90}^{°}$ but less than ${180}^{°}$ is called an obtuse angle.

(v) An angle whose measure is ${180}^{°}$ is called a straight angle.

(vi) An angle whose measure is more than ${180}^{°}$ is called a reflex angle.

(vii) Two angles are complementary if their sum is ${90}^{°}$.

(viii) Two angles are supplementary if their sum is ${180}^{°}$.

(ix) Two angles having a common vertex and a common arm are called adjacent angles if their uncommon arms are on either side of the common arm.

(x) Two adjacent angles are said to form a linear pair of angles if their non-common arms are two opposite rays.

(xi) Two angles are pairs of vertically opposite angles if their arms form two pairs of opposite rays.

2. Lines:

(i) If two lines intersect, then vertically opposite angles are equal.

(ii) If a transversal intersects two parallel lines, then each pair of

(a) corresponding angles are equal

(b) alternate interior angles are equal

(c) interior angles on the same side of the transversal are supplementary.

(iii) If a transversal intersects two lines such that, either

(a) any one pair of corresponding angles are equal, or

(b) any one pair of alternate interior angles are equal, or

(c) any one pair of interior angles on the same side of the transversal are supplementary then the lines are parallel.

(iv) Lines that are parallel to a given line are parallel to each other.