Math, asked by amishwankahde, 1 month ago

How many diagonals will a regular polygon have if it’s each exterior angle is 120 degree
?

Answers

Answered by pranav3716
1

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

Answered by whamwham
3

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:

\bf{\dfrac{n(n-3)}{2}

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:

\bf{\dfrac{Sum\:of\:all\:exterior\:angles}{Measure\:of\:an\:exterior\:angle}

\sf{=\dfrac{360}{120}

\sf{=3}

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:

\sf{\dfrac{3(3-3)}{2}

\sf{=\dfrac{3\times0}{2}

\sf{=\dfrac{0}{2}

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.

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