Lines &: Angles
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 1o to 360o. The symbol of angle is ∠.
Angles less than 90o are called Acute Angles. For example: 20o, 30o, 85o, 65o, etc.
Angles more than 90o are called Obtuse Angles. For example: 95o, 100o, 110o, 165o, etc.
Angle equal to 90o is called Right Angle.
Angle equal to 180o is called Straight Angle.
Angles greater than 18090o are called reflex angles. For example 190o is a reflex angle.
When the sum of two angles is equal to 90o, they are called complementary angles. Both angles are called complementary to each others. For example 30o and 60o, 40o and 50o, 20o and 70o, etc. are complementary angle since their sum is equal to 90o.
When the sum of two angles is equal to 180o, then they are called supplementary angles. Both angles are called supplementary to each others. For example 100o and 80o, 30o and 150o, etc. are complementary angle.
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 of Angles
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 180o.
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.
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).