Class 8 Exam  >  Class 8 Notes  >  NCERT Solution (Ex-3.2) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8

NCERT Solution (Ex-3.2) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8 PDF Download

Understanding Quadrilaterals

Exercise 3.2

Question 1: Find x in the following figures:

Answer 1:
(a) Here, 125o+m=180o   [Linear pair]


 m=180o-125o = 55o
and 125o+n =180o           [Linear pair]
n =180o-125o = 55o
Exterior angle xo = Sum of opposite interior angles
xo = 55o+55o =110o

(b) Sum of angles of a pentagon = (n - 2)x180o
= (5 - 2)x180o
= 3x180o = 540o

By linear pairs of angles,

Adding eq. (i), (ii), (iii), (iv) and (v),

Question 2:
Find the measure of each exterior angle of a regular polygon of:
(a) 9 sides

(b) 15 sides 

Answer 2:
(i) Sum of angles of a regular polygon = (n-2)x180o
= (9-2)x180o = 7x180o =1260o

Each interior angle= Sum of interior angles / Number of sides =1260o/9 =140o

Each exterior angle = 180o-140o = 40o

(ii) Sum of exterior angles of a regular polygon = 360o
Each interior angle = Sum of interior angles/Number of sides = 360o/15 =24o

Question 3:
How many sides does a regular polygon have, if the measure of an exterior angle is 24o?

Answer 3:
Let number of sides be n.

Hence, the regular polygon has 15 sides.

Question 4:
How many sides does a regular polygon have if each of its interior angles is 165?

Answer 4:
Let number of sides be n.
Exterior angle = 180o-165o=15o
Sum of exterior angles of a regular polygon = 360o

Hence, the regular polygon has 24 sides.

Question 5:
(a) Is it possible to have a regular polygon with of each exterior angle as 22
o?
(b) Can it be an interior angle of a regular polygon? Why?

Answer 5:
(a) No. (Since 22 is not a divisor of 360o )
(b) No, (Because each exterior angle is 180o - 22o =158o, which is not a divisor of 360o )

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 6:
(a) The equilateral triangle being a regular polygon of 3 sides has the least measure of an interior angle of 60o .

 Sum of all the angles of a triangle = 180o

 x+x+x= 180

 3x=1800

 x=60o

(b) By (a), we can observe that the greatest exterior angle is 1800 - 600 =1200.

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FAQs on NCERT Solution (Ex-3.2) - Chapter 3: Understanding Quadrilaterals, Maths, Class 8

1. What is a quadrilateral?
Ans. A quadrilateral is a four-sided polygon. It is a closed figure with four sides, four vertices, and four angles.
2. What are the types of quadrilaterals?
Ans. There are different types of quadrilaterals, such as trapezium, kite, parallelogram, rectangle, rhombus, and square.
3. How do you identify a parallelogram?
Ans. A parallelogram is a quadrilateral with two pairs of parallel sides. To identify a parallelogram, we need to check if opposite sides are parallel and if opposite angles are congruent.
4. What is the difference between a rhombus and a square?
Ans. A rhombus is a quadrilateral with all sides equal, while a square is a quadrilateral with all sides equal and all angles equal to 90 degrees. In other words, a square is a special type of rhombus.
5. How can we calculate the area of a quadrilateral?
Ans. The formula for calculating the area of a quadrilateral depends on its type. For example, the area of a parallelogram is base multiplied by height, while the area of a trapezium is the sum of the parallel sides multiplied by the perpendicular distance between them, divided by 2.
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