CBSE Class 7 Mathematics – 13. Lines and Angles (Notes)

Revision Notes on Line and Angle

Learning Goal

1. Angle & Types of Angles

   – Acute, obtuse, right, and straight angles.

   – Complementary and supplementary angles.

2. Properties of Angles

   – Angles on a straight line add up to 180 degrees.

   – Angles around a point add up to 360 degrees.

3. Pair of Angles

   – Adjacent angles

   – Vertical angles

   – Linear pair of angles

   – Complementary and supplementary pairs

 

Point

A geometrical element which has no dimensions (length &breadth) is called point.

Line segment: –    A shape joining two points is called line segment.

Properties of line segment: –       

A line segment has two ends point.     

It can’t extend by any sides.        

Line: – A line segment which is extended by both sides is called line.

Properties of line: –   

Line has no ends point.

Line is extended by both sides.   

Ray – A line segment which is extended by one side is called ray.

Properties of ray: –   

Ray has one end point.

Ray is extended by one side.   

Angles

When two line segment meets on a point,then inclination (झुकाव)  between them is called angle.

It is denoted by ∠ .

Two rays with a common end point form an angle.

The common end point is called vertex . In figure  B is vertex (शीर्ष).

Every angle has two arms. In figure AB and CB are arms of angle.

In first figure ABC or CBA is angle. It can be written as ∠ABC or ∠CBA

In second figure ∠XOY, ∠ZOW, ∠YOW and ∠XOZ are angles. 

The unit of measurement of an angle is degree(°)

Related Angles OR Pair Angle

1. Complementary Angles

2. Supplementary Angles

3. Adjacent Angles

4. Linear Pair

5. Vertically Opposite Angles

1. Complementary Angles

If the sum of two angles is 90° then they are called complementary angles.

∠A + ∠B = 90⁰

OR ∠A  = 90⁰– ∠B

2. Supplementary Angles

If the sum of two angles is 180° then they are called supplementary angles.

If two angles are supplementary then they are the supplement to each other.

∠A + ∠B = 180⁰

OR ∠A  = 180⁰– ∠B

3. Adjacent Angles

If two angles which have a common vertex, a common arm and non-common arms are opposite of common arm than they are called adjacent agles.

Adjacent angles have-

A common vertex.

A common arm.

A non-common arm could be on either side of the common arm.

4. Linear Pair

A pair of adjacent angles whose non-common arm makes a single line i.e. they are the opposite rays.

A linear pair is also a pair of supplementary angles amd their sum is 180°.

The above pair of angles is –

Adjacent, as they have one common arm.

Supplementary, as the sum of two angles, is 180°.

The linear pair, as the sum is 180° and the non – common arms are opposite rays.

5. Vertically Opposite Angles

When two lines intersect each other then the angle form opposite of each other is called vertically opposite angles. 

∠a and ∠b is pair of vertically opposite angles.

∠n and ∠m is pair of vertically opposite angles.

Vertically opposite angles are equal.