1.

How many sides does a regular polygon have if each of its interior angles is 140 ?​

Answer»

\large\underline{\sf{Solution-}}

GIVEN that,

↝  Each interior angle of a regular polygon is 140°.

Let assume that

↝ Exterior angle of a regular polygon be x°.

and

↝ Number of SIDES of a regular polygon be 'n'.

We know,

Interior angle and exterior angle of a regular polygon is connected by the relationship

\boxed{ \tt{ \: Interior \: angle + Exterior \: angle = 180 \degree \: }}

So, using this, relationship

\rm :\longmapsto\:140\degree + x = 180\degree

\rm :\longmapsto\:x = 180\degree - 140\degree

\rm \implies\:\boxed{ \tt{ \: x \: = \: 40\degree \: }}

Further, We know that

Number of sides and exterior angle of a regular polygon is connected by the relationship

\boxed{ \tt{ \: Number \: of \: sides = \frac{360\degree}{Exterior \: angle} \: }}

So, using this release, we GET

\rm :\longmapsto\:n \: = \: \dfrac{360\degree}{40\degree}

\rm \implies\:\boxed{ \tt{ \: n \: = \: 9 \: }}

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Additional Information :-

Properties of a triangle

A triangle has three sides, three angles, and three vertices.

The sum of all internal angles of a triangle is 180°. 

The sum of any two sides of a triangle is GREATER than the the third side.

The side opposite to the LARGEST angle is always greater.

The angle opposite to longest side is always greater.

Exterior angle of the triangle is equal to the sum of its interior opposite angles.

Sum of all exterior angles of a triangle is 360°


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