**Angles: **When two straight lines meet at a point they form an angle. In the figure, the angle is represented as ∠AOB. OA and OB are the arms of ∠AOB. Point O is the vertex of ∠AOB. The amount of turning from one arm (OA) to other (OB) is called the measure of the angle (AOB).

**Right angle**: An angle whose measure is 90^{o }is called a right angle. ∠ BOA is a right angle in the figure.

**Acute angle**: An angle whose measure is less then one right angle (i.e., less than 90^{o}), is called an acute angle.

**Obtuse angle**: An angle whose measure is more than one right angle i. e. 90^{o} and less than two right angles

(i.e., less than 180^{o} and more than 90^{o}) is called an obtuse angle.

**Reflex angle**: An angle whose measure is more than 180^{o} and less than 360^{o} is called a reflex angle.

**Complementary angles**: If the sum of the two angles is one right angle (i.e., 90^{o}), they are called complementary angles. Therefore, the complement of an angle θ is equal to 90° − θ. ∠AOC & ∠ COB are **Complementary angles.**

**Supplementary angles: **Two angles are said to be supplementary, if the sum of their measures is 180^{o}. Here ∠BOC & ∠ COA are **Supplementary angles.**

**Example: **Angles measuring 130o and 50o are supplementary angles. Two supplementary angles are the supplement of each other. Therefore, the supplement of an angle θ is equal to 180° − θ.

· The sum of all the angles round a point is equal to 360°.

· If two lines intersect, then the vertically opposite angles are equal.

Angle a = angle b (vertically opposite angle)

· If a transversal intersects two parallel lines, then each pair of corresponding angles are equal.

· **Other facts :**

**1. ****Linear pair : **

a + b = 180°

**2. ****Vertical opposite angles:**

a = c & b = d e = g & f = h

**3. ****Alternate angles:**

c = e, d = f

**4. ****Sum of Interior angle is always 180****°****:**

c + f = d + e = 180°

**Bisector of an angle**: If a ray or a straight line passing through the vertex of that angle, divides the angle into two angles of equal measurement, then that line is known as the Bisector of that angle.

A point on an angle is equidistant from both the arms.

In the figure, Q and R are the feet of perpendiculars drawn from P to OB and OA. It follows that

PQ = PR.