BlogNCERTNCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.2

Ex 3.2 Class 8 Maths Question 1.
Find x in the following figures.
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q1
Solution:
(a) We know that the sum of all the exterior angles of a polygon = 360°
125° + 125° + x = 360°
⇒ 250° + x = 360°
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q1.1
x = 360° – 250° = 110°
Hence x = 110°
(b) Here ∠y = 180° – 90° = 90°
NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q1.2
and ∠z = 90° (given)
x + y + 60° + z + 70° = 360° [∵ Sum of all the exterior angles of a polygon = 360°] ⇒ x + 90° + 60° + 90° + 70° = 360°
⇒ x + 310° = 360°
⇒ x = 360° – 310° = 50°
Hence x = 50°

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    Ex 3.2 Class 8 Maths Question 2.
    Find the measure of each exterior angle of a regular polygon of
    (i) 9 sides
    (ii) 15 sides
    Solution:
    (i) We know the sum of all the exterior angles of polygon = 360°
    Measure of each angle of 9 sided regular polygon = \(\frac { 360 }{ 9 }\) = 40°
    (ii) Sum of all the exterior angles of a polygon = 360°
    Measure of each angle of 15 sided regular polygon = \(\frac { 360 }{ 15 }\) = 24°

    Ex 3.2 Class 8 Maths Question 3.
    How many sides does a regular polygon have if the measure of an exterior angle is 24°?
    Solution:
    Sum of all exterior angles of a regular polygon = 360°
    Number of sides
    NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q3
    Hence, the number of sides = 15

    Ex 3.2 Class 8 Maths Question 4.
    How many sides does a regular polygon have if each of its interior angles is 165°?
    Solution:
    Let re be the number of sides of a regular polygon.
    Sum of all interior angles = (n – 2) × 180°
    and, measure of its each angle
    NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q4
    Hence, the number of sides = 24

    Ex 3.2 Class 8 Maths Question 5.
    (a) Is it possible to have a regular polygon with measure of each exterior angle a is 22°?
    (b) Can it be an interior angle of a regular polygon? Why?
    Solution:
    (a) Since, the sum of all the exterior angles of a regular polygon = 360° which is not divisible by 22°.
    It is not possible that a regular polygon must have its exterior angle 22°.
    (b) Sum of all interior angles of a regular polygon of side n = (n – 2) × 180°
    NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q5
    not a whole number.
    Since number of sides cannot be in fractions.
    It is not possible for a regular polygon to have its interior angle = 22°.

    Ex 3.2 Class 8 Maths 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?
    Solution:
    (a) Sum of all interior angles of a regular polygon of side n = (n – 2) × 180°
    The measure of each interior angle
    NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 Q6
    The minimum measure the angle of an equilateral triangle (n = 3) = 60°.
    (b) From part (a) we can conclude that the maximum exterior angle of a regular polygon = 180° – 60° = 120°.

    NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A1

    NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A1.1

    NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A2

    NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A3

    NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A4

    NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A5

    NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.2 A6
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