NCERT Class 8 Mathematics Solutions: Chapter 3 –Understanding Quadrilaterals Exercise 3.2 Part 2

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Given this figure find the Interior angle and External angle

A Figure is Find the Interior Angle and External Angle

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Question: 2 Find the measure of each exterior angle of a regular polygon of:

(a) 9 sides

(b) 15 sides

Answer:

Sum of angles a regular polygon having side

(a) 9 Sides

Each interior angle =

Each exterior angle =

(b) 15 Sides

Each interior angle =

Each exterior angle =

Question: 3 How many sides does a regular polygon have, if the measure of an exterior angle is

Answer:

Let number of sides be

Sum of the measure of exterior angles of a regular polygon

Number of sides

Hence, the regular polygon has 15 sides.

Question: 4 How many sides does a regular polygon have if each of its interior angles is

Answer:

Let number of sides be n.

Exterior angle =

Sum of exterior angles of a regular polygon

Number of sides

Hence, the regular polygon has sides.

Question: 5

(a) Is it possible to have a regular polygon with of each exterior angle as?

(b) Can it be an interior angle of a regular polygon? Why?

Answer:

(a) Exterior angle

=

No, we can't have a regular polygon with each exterior angle as 22° as it is not divisor of 360.

(b) Interior angle

Interior angle =

No, we can't have a regular polygon with each Interior angle as 158° as it is not divisor of 360.

Question: 6

(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?

Answer:

(a) The equilateral triangle being a regular polygon of 3 sides has the least measure of an interior angle of 60.

Sum of all the angles of a triangle

(b) By (a), we can observe that the greatest exterior angle is