Question

Two alternate side of a regular polygon when produced meet at 120 deg. Find each exterior angle of polygon. (2)
the number of side of polygon.

Answer 1

when two alternate sides are produced, they will create a triangle . let say triangle ABC is created where B and C are two consecutive vertex of the regular polygon . and produced sides from B and C meets at A to make angle of 120 deg as mentioned in question.

now, let assume the number of sides in a polygon is n.

hence value of each exterior angle of the regular polygon = 360/n. ......(1)

now in triangle ABC ,
angle A= 120 deg
angle B =angle C =exterior angle of regular polygon
hence angle B=angle C=360/n ......(2)
applying angle sum property in ABC .we get,
ang A +ang B +ang C =180
120 +360/n +360/n =180 .......(3)
on solving equation 3 we get
n=12
substituting value of n in equation 1 we get
ext. angle =360/12 =30 deg

therefore each ext. angle of regular polygon is 30 deg and number of sides in the regular polygon is 12.

hope it helps

Answer 2

Answer:

In a regular polygon all the exterior angles have the same measure.

When two alternate sides of a polygon are extended a triangle.

If AB, BC and CD are the sides of a regular polygon and AB and CD when produced meet at P forming a right triangle.

Now, in △CPB,∠PCB=∠PBC=45

o

Therefore, exterior angle of the polygon = 45

o

Exterior angle of a regular polygon =

n

360

o

=>45

o

=

n

360

o

=>n=8

Number of sides of the polygon = 8