How many diagonals will a regular polygon have if it’s each exterior angle is 120 degree
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Answers
Answer:
0 is the answer as the polygon is a triangle b coz
sum of exterior angles = 360°
So,
120n= 360
n=360/120
n=3
Hence it's a traingle
but triangle doesn't have diagonals
Given:
- the polygon is regular
- each exterior angle = 120°
To find:
- the number of diagonals
Solution:
If we are given the number of sides of a polygon, the number of diagonals in the polygon is:
with 'n' as the number of sides.
But we are given just the exterior angle. We know that the polygon is regular, so:
- all its exterior angles would be equal.
- the sum of the exterior angles of any polygon is 360°
Therefore, the number of sides in this polygon would be:
The number of sides in this polygon is 3 which means it is a triangle. We know that a triangle does not have diagonals, but to prove it to the examiner, we need to justify it by using the formula.
So the number of diagonals in it would be:
0/2! It does not have any diagonals.
Therefore, a regular polygon with its exterior angles as 120° has zero diagonals.
Important Terms
- A polygon
It is a closed shape made up of any number of line segments.
Polygons: triangle, quadrilaterals, pentagons etc.
NOT polygons: circle, other open or curved shapes
- A diagonal
It is line formed by connecting two opposite vertices of a polygon.
- An exterior angle
An angle formed between one extended side of a polygon and its adjacent side is an exterior angle.