Draw rough diagrams of two angles which have (a) One point common (b) Two points in common (c) Three points in common (d) Four points in common (e) One ray in common.

Step 1. (a) Draw rough diagrams of two angles that have one point in common.

The diagram of two angles such that they have one point in common is as shown:

Hence, $\angle \mathrm{AOB}$ and $\angle \mathrm{BOC}$ have $\mathrm{O}$ in common.

Step 2. (b) Draw rough diagrams of two angles that have two points in common.

The diagram of three angles such that they have two points in common are as shown:

Hence, $\angle \mathrm{MON}$ and $\angle \mathrm{ONR}$ have $\mathrm{O}$ and $\mathrm{N}$ in common.

Step 3. (c) Draw rough diagrams of two angles that have three points in common.

No such angles are formed.

Step 4. (d) Draw rough diagrams of two angles that have four points in common.

No such angles are formed.

Step 5. (e) Draw rough diagrams of two angles that have one ray in common.

The diagram of two angles such that they have one ray in common is shown below:

Hence, ray $\overrightarrow{\mathrm{OB}}$ is common to $\angle \mathrm{AOB}$ and $\angle \mathrm{BOC}$.