Question

Draw a rough diagram of two angles such that they have two points in common.

Answer 1

Hint: There is no particular formula or particular way present as such to solve such type of question. A simple logical idea can help us start the construction. To be precise start with two angles having one point in common and then constructing two points in common won’t be a difficult issue.

Complete step by step solution:
We have been asked in this question to draw a rough diagram of two angles which have two points in common.
In this type of question we need to visualize how angles drawn or placed together can have two points in common.
Generally two angles can have one point in common or more than one points in common.
When one point is common two angles are joint to each other at one point as in the figure.

Two angles $\angle {\text{AOB}}$ and $\angle {\text{POR}}$ have point O in common.
Now to get two points in common we can try to get a segment common in two angles. Now all we have to try is to construct a segment which is common in both angles.
Following can be the construction of such visualization

Hence we have two points angles as $\angle {\text{POQ}}$ and angle $\angle {\text{QOR}}$ which have point O and point Q in common to both the angles.
Hence we have constructed a diagram which has two points in common to two angles.

Note: Like this question there are many more questions where we can be told to find the more than two points in common between two angles. The basic logic to be used in this kind of questions then is to start extending or adding points to the segment that is common to both the angles which will help you get required points in common.