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**Class 8 CBSE Mathematics Guide and
NCERT Solutions **

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**Chapter 3 Understanding
Quadrilaterals **

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__NCERT Solutions
of Understanding Quadrilaterals Exercise 3.2__

__NCERT Solutions of Understanding Quadrilaterals Exercise 3.2__

Question 1: Find

*x*in the following figures.__Solution__:

(a)

We know that the sum of all exterior angles of any polygon
is 360º.

Therefore, 125

^{O}+ 125^{O }+*x*= 360^{O}
⇒

*x*= 110^{O}
(b)

⇒ 60° + 90° + 70° +

*x*+ 90° = 360° (∴ 180^{O}– 90^{O}= 90^{O})
⇒ 310° +

*x*= 360°
⇒

*x*= 50°
Question 2: Find the measure of each exterior angle of a regular
polygon of

(i) 9 sides

(ii) 15 sides

__Solution__: We know total measures of all exterior angles = 360

^{O}

Also, each exterior
angle of a regular polygon has the same measure.

(i) Total number of
sides = 9

∴ Measure of each exterior angle =
360

^{O}÷ 9 = 40^{O}
(ii) Total number of
sides = 15

∴ Measure of each exterior angle =
360

^{O}÷ 15 = 24^{O}
Question 3: How many sides does a regular polygon have if the
measure of an exterior angle is 24°?

__Solution__: We know total measures of all exterior angles = 360

^{O}

Given that each
exterior angle of the regular polygon = 24

^{O}
∴ Number of sides = 360

^{O}÷ 24^{O}= 15
Question 4: How many sides does a regular polygon have if each
of its interior angles is 165°?

__Solution__: Measure of each interior angle = 165°

⇒ Measure of each
exterior angle = 180° − 165° = 15°

⇒ Sum of all exterior angles of any
polygon = 360º

∴ Number of sides = 360

^{O}÷ 15^{O}= 24
Question 5: (a) Is it possible to have a regular polygon with
measure of each exterior angle as 22°?

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

__Solution__:

(a) The sum of all exterior angles
of all polygons is 360º. In a regular polygon, each exterior angle is of the
same measure. Hence, a regular polygon is possible only if 360º is a perfect
multiple of the given exterior angle. In the given case the answer is ‘No’.
(Since; 22° is not divisor of 360º).

(b) Given that interior angle = 22°

⇒ Exterior angle = 180° − 22° = 158°

In the given case the answer is ‘No’
because 158° is not divisor of 360º.

Question 6: (a) What is the minimum interior angle possible for
a regular polygon?

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

__Solution__:

We know, measure of each exterior angle = 360

^{O}÷ (Number of sides of a regular polygon)
Hence, ‘Maximum Exterior Angle’ will be of a regular polygon with minimum
sides and the same will have a minimum ‘Interior Angle’. Because,

Interior angle = 180º − Exterior Angle.

(a) The equilateral triangle being a regular polygon with only 3 sides has
the least measure of Interior Angle 60

^{O}
(b) From the above we can see that the greatest Exterior Angle = 180º − 60º
= 120º

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