Ex.3.2 Q6 Understanding Quadrilaterals Solution - NCERT Maths Class 8

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Question

(a) What is the minimum interior angle possible for a regular polygon? Why?

(b) What is the maximum exterior angle possible for a regular polygon?

Text Solution

What is Known?

We know polygons according to the number of sides (or vertices) they have.

What is Unknown?

Minimum interior angle possible for a regular polygon.

Maximum exterior angle possible for a regular polygon.

Reasoning:We know that the sum of measure of interior angle of triangle is  \(={\rm{18}}0^\circ  \)

Equilateral triangle is regular polygon having maximum exterior angle because it consists of least number of sides.

Steps: 

(a) What is the minimum interior angle possible for a regular polygon? Why?

Consider a regular polygon having the least number of sides (i.e., an equilateral triangle).

We know Sum of all the angles of a triangle \(= {\rm{18}}0^\circ  \)

\[\begin{align}x + x + x{\rm{ }}& = {\rm{ 18}}0^\circ \\{\rm{3}}x &= {\rm{18}}0^\circ \\x &= \frac{{{\rm{18}}0^\circ }}{3}\\x &= {\rm{6}}0^\circ\end{align}\]Thus, minimum interior angle possible for a regular polygon\(= 60^\circ \)

(b) What is the maximum exterior angle possible for a regular polygon?

We know that the exterior angle and an interior angle will always form a linear pair. Thus exterior angle will be maximum when interior angle is minimum.

Exterior angle

\[\begin{align}&= {\rm{18}}{0^{\rm{\circ}}} - \,\,{\rm{6}}0^\circ \\&={120^{\rm{\circ}}}.\end{align}\]

Therefore, maximum exterior angle possible for a regular polygon is \(120^\circ\)

Equilateral triangle is a regular polygon having maximum exterior angle because it consists of least number of sides.

  
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