NCERT Class 8 Mathematics Solutions: Chapter 3 –Understanding Quadrilaterals Exercise 3.1 Part 5

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Given this figure of sides of regular polygon

Sides of Regular Polygon

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Question: 5 What is a regular polygon? State the name of a regular polygon of:

(a) 3 sides

(b) 4 sides

(c) 6 sides

Answer:

A regular polygon: A polygon having all sides of equal length and all angles are equal is known as regular polygon.

(a) 3 sides:

Polygon having three sides is called a Triangle.

(b) 4 sides:

Polygon having four sides is called a Quadrilateral.

(c) 6 sides

Polygon having six sides is called a Hexagon.

Question: 6 Find the angle measures x in the following figures:

(a)

Image

This Figure is a Quadrilateral

(b)

Image

This Figure is Perpendicular

(c)

Image

Pentagon Figure

(d)

Image

Regular Pentagon Figure

Answer:

(a) The figure is having 4 sides. Hence, it is a quadrilateral.

Using angle sum property of a quadrilateral,

Image:

The Figure is Having 4 Sides, It is a Quadrilateral

(b) The figure is having 4 sides. Hence, it is a quadrilateral. Also, one side is perpendicular forming right angle.

Using angle sum property of a quadrilateral,

Image:

One Side is Perpendicular Forming Right Angle

(c) The figure is having 5 sides. Hence, it is a pentagon.

Image:

This Figure is Pentagon

First base interior angle

Second base interior angle

There are 5 sides,

(d) The figure is having 5 equal sides. Hence, it is a regular pentagon. Thus, it’s all angles are equal.

Image:

This Figure is Regular Pentagon

Angle sum of a polygon

There are 5 sides,

Hence, each interior angle is