# Lines & Angles

## Introduction: Important Definitions

**Angle:** A figure formed by two rays having a common end point is called an angle. Rays are called sides of the angle. Common end point which is shared by both the sides (rays) is called vertex of the angle. Angles are usually measured in degree. Angle may be equal to 1^{o} to 360^{o}. The symbol of angle is ∠.

**Acute Angle:** Angles less than 90^{o} are called Acute Angles. For example – 20^{o}, 30^{o}, 85^{o}, 65^{o}, etc.

**Obtuse Angle:** Angles more than 90^{o} are called Obtuse Angles. For example – 95^{o}, 100^{o}, 110^{o}, 165^{o}, etc.

**Right Angle:** Angle equal to 90^{o} is called Right Angle.

**Straight Angle:** Angle equal to 180^{o} is called Straight Angle.

**Reflex Angle:** Angles greater than 18090^{o} are called reflex angles. For example 190^{o} is a reflex angle.

### Complementary Angles:

When the sum of two angles is equal to 90^{o}, they are called complementary angles. Both angles are called complementary to each others. For example 30^{o} and 60^{o}, 40^{o} and 50^{o}, 20^{o} and 70^{o}, etc. are complementary angle since their sum is equal to 90^{o}.

### Supplementary Angles:

When the sum of two angles is equal to 180^{o}, then they are called supplementary angles. Both angles are called supplementary to each others. For example 100^{o} and 80^{o}, 30^{o} and 150^{o}, etc. are complementary angle.

**Adjacent Angles:** When two angles have a common arm and common vertex and their non-common arm are the either side of common arm, then they are called adjacent angles.

#### Conditions of adjacent angles:

- They have one arm common
- They have common vertex
- Non-common arms are the either side of common arm.
- Common arm should be in the middle of rest two sides.

In the given figure ‘O’ is the common vertex and OB is the common arm. Hence, ∠a and ∠b are called the adjacent angles.

**Linear Pair:** A pair of adjacent angles is called linear pair, if their two non-common arms are opposite rays.

Here adjacent ∠A and ∠B are linear pair The angle sum of a linear pair is equal to 180^{o}.

**Vertically Opposite Angles:** When two straight lines intersect, then four angles are formed. The opposite angles are called vertically opposite angles. The vertically opposite angles are always equal.

In the given figure, ∠1 and ∠2,and ∠3 and ∠4 are called opposite angle.

**Transversal:** A line is called transversal line when it cuts two lines at distinct points.

In the given picture AB is the transversal line which cuts CD and EF at two different (distinct points).