[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Before answering the given question, you should know the difference between polygon and regular polygon.
- Polygon :- It is closed figure constitute of straight line having different measurements and also having varies angles.
- Regular polygon :- It is also a closed figure constitute of straight lines which having equal measuresment and all the angles of the given polygon are equal .
There are different types of polygon based on the sides :-
- A polygon having 3 sided called triangle ,having 4 sides called quadrilateral ,having 5 sides pentagon and so on.
Let's Begin :-
I have thought to make a 4 side polygon that is quadrilateral.
Steps of construction :-
- Step - 1 :- Draw a 5 cm line AB horizontally
- Step - 2 :- Then , From a point B, Draw a Vertical line of 5 cm and named it BC
- Step - 3 :- Then, From a point C, Draw a horizontal line of 5 cm and named it CD
- Step - 4 :- Now, join the line AD
- Step - 5 :- Measure all the angles form by the 4 sides of the quadrilateral.
Result :- All the angles are equal that is 90° each.
Conclusion :- The above figure is square as it is having equal sides and angles.
Now, we have to find the sum of the angles of the polygon :-
Here,
- All angles are equal in measure 90°
Therefore,
The sum of the angles of the given polygon
[tex]\sf{ = 90{\degree} + 90{\degree} + 90{\degree} + 90{\degree} }[/tex]
[tex]\sf{ = 180{\degree} + 90{\degree} + 90{\degree} }[/tex]
[tex]\sf{ = 270{\degree} + 90{\degree} }[/tex]
[tex]\sf{ = 360{\degree} }[/tex]
Hence, The sum of the angles of the above polygon is 360° .
