Different Types of Angles-Adjacent, Acute, Right, Obtuse, Straight, Reflex

Have you started learning lines and angles chapter read basics of Different types of angles-Acute, Right, Obtuse, Straight, Reflex, vertically opposite,co-interior, complementary and supplementary angles. To know more about lines and angles read my article carefully.

Lines and Angles Introduction

Ray:- It is a straight line which starts from a fixed point and moves in the same direction.The given figure shows a ray AB with initial fixed point A and moving in direction AB.

LINE SEGMENT:- It is a straight line with its both ends fixed. The given figure shows a line segment, whose both ends A and B are fixed.

ANGLE:- An angle is formed when two line segments or two rays have a common endpoint. The two line segments forming an angle are called the arms of the angle whereas their common endpoint is called the vertex of the angle. The adjacent figure represents an angle ABC. AB and BC are the arms of the angle and their common point B is the vertex.

Different Types of Angles-Adjacent, Acute, Right, Obtuse, Straight, Reflex

Angles About a Point

: If a number of angles are formed about a point, their sum is always 360.

In the given figure :

Angle AOB +BOC+COD+DOE+EOA=360

Adjacent Angles

Two angles are said to be

Adjacent angles if:-

a) They have common vertex,

b) They have common arm and

c) The other two arms of the two angles lie on opposite sides of the common arm.

The adjoining figure shows a pair of adjacent angles

Because (a) they have common vertex (O).

(b) they have a common arm (OB) and

On opposite sides of the common arm OB.

Vertically Opposite Angles

When two straight lines intersect each other four angles are formed.

The pair of angles which lie on the opposite sides of the point of intersection are called vertically opposite angles.

In the adjoining figure, two straight lines AB and CD intersect each other at point O. Angles AOD and BOC forms

one pair of vertically opposite angles, whereas angles AOC and BOD form another pair of vertically opposite angles.

Vertically opposite angles are always equal.

i.e. angle AOD= angle BOC

angle AOC = angle BOD

Complementary And SupplementaryAngles

1. Two angles are called complementary angles, if their sum is one right angle, i.e., 90. Each angle is called the complement of the other.

e.g. 20 and 70 are complementary angles because 20 + 70 = 90

Clearly, 20 is the complement of 70 and 70 is the complement of 20

Thus the complement of angle 53= 90-53=37

2. Two angles are called supplementary angles if their sum is two right angles, i.e. 180. Each angle is called the supplement of the other.

e.g. 30 and 150 are supplementary angles because 30 + 150 = 180

Clearly, 30 is the supplement of 150 and vice versa

Thus the supplement of 105 = 180 – 105 = 75.

You can also Read- Basics of Unitary Method.

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