Question

Draw a rough diagram of two angles such that they have:
I). One common point
II). Two common points
III). three common points
IV). Four common points

Answer 1

Hint: In geometry, an angle is formed by two rays meeting at a common endpoint. An angle is represented by the symbol $\mathrm{\angle }$. Angles are measured in degrees, using a protector.

In the above figure,
The angle is $\mathrm{\angle }ABC$.
The angle has two rays $\overrightarrow{BA}$ and $\overrightarrow{BC}$.
These two rays $\overrightarrow{BA}$ and $\overrightarrow{BC}$ start with a common point B.
Hence, the angle has one common point B.

Complete step-by-step solution:
I). Two angles have one common point:
If two angles have one common point then, their endpoint is the same.

In the above figure, there are two angles.
The first angle is $\mathrm{\angle }ABD$ and the second angle is $\mathrm{\angle }DBC$.
In these two angles, there is only one common point ‘B’.
II). Two angles have two common points:
Since the angle has only one endpoint, we cannot have two angles with two points in common.
It is not possible.
III). Two angles have three common points:
Since the angle has only one endpoint, we cannot have two angles with three points in common.
It is not possible.
IV). Two angles have four common points:
Since the angle has only one endpoint, we cannot have two angles with four points in common.
It is not possible.

Note: Remember that two or more angles have only one endpoint. So, we can say that two or more angles have only one common point.
Parts of an Angle:

Arms: The two rays joining to form an angle are called arms of an angle. Here, OA and OB are the arms of the $\mathrm{\angle }ABC$.
Vertex: The common end point at which the two rays meet to form an angle is called the vertex. Here, the point O is the vertex of $\mathrm{\angle }ABC$.