How to construct a regular Pentagon?

Understand the Construction of regular Pentagon. Click on the link to Watch the VIDEO explanation: Watch Video

Construction of a Regular Pentagon
There are two method for constructing a regular pentagon. Select one from below..
Method 1
To construct a regular pentagon given side AB is equal to 4 cm
Constructing triangle AOB, AB is equal to 4 cm,
Angle OAB is equal to angle OBA is equal to 54 degrees
A pentagon subtends 360 degrees by 5 is equal to 72 degrees at the centre of the circle, i.e., at O.
OA is equal to OB since they are the radii of the circle
Therefore, angle OAB is equal to angle ABO which is equal to 180 degrees minus 72 degrees by 2 this is equal to 54 degrees.
The steps of construction are as follows
Draw AB is equal to 4 cm
At A, make angle BAX is equal to 54 degrees using a protractor.
Construct the perpendicular bisector of AB which cuts AX at O.
With O as centre and radius AO, draw a circle
With centre B and radius is equal to 4 cm, cut the circle at C.
Again, with centre C and the same radius of 4 cm, cut the circle at D.
Similarly, with centre D cut the circle at E.
Join BC, CD, DE and AE.
Therefore, ABCDE is the required regular pentagon.
Method 2
Constructing each interior angle equal to 108 degrees
Exterior angle of a regular pentagon is equal to 360 degrees by 5 which is equal to 72 degrees.
Therefore, Each interior angle is equal to 180 degrees minus 72 degrees which is equal to 108 degrees.
Proceed as stated with the construction
Draw AB is equal to 4 cm
Using a protractor, make angle ABX is equal to angle BAY is equal to 108 degrees.
Cut BX and AY at C and E respectively, So that BC is equal to AE is equal to AB is equal to 4 cm.
With centre C and E and radius of 4 cm, draw two arcs which intersect at D.
Join CD and DE
Therefore, ABCDE is the required regular pentagon.