NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals InText Questions

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals InText Questions

These NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals InText Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals InText Questions

Try These (Page No. 43)

Take a regular hexagon Fig 3.10.

Question 1.
What is the sum of the measures of its exterior angles x, y, z, p, q, r?
Solution:
∠x + ∠y + ∠x + ∠z + ∠p + ∠q + ∠r = 360°
[∵ Sum of exterior angles of a polygon = 360°]

Question 2.
Is x = y = z = p = q = r? Why?
Solution:
Since, all the sides of the polygon are equal.
∴ It is a regular hexagon.
So, its interior angles are equal.
∴ x = (180° – a)
y = (180° – a)
z = (180° – a)
p = (180° – a)
q = (180° – a)
r = (180° – a)
∴ x = y = z = p = q = r

Question 3.
What is the measure of each?
(i) exterior angle
(ii) interior angle
Solution:
(i) x + y + z = p + q = r = 360° [sum of exterior angles = 360°]
and all these angles are equal
∴ Measure of each exterior angles = 360∘/6 = 60°

(ii) ∵ Exterior angle = 60°
∴ 180° – 60° = Interior angle
or 120° = Interior angle
or Measure of interior angle = 120°

Question 4.
Repeat this activity for the cases of
(i) a regular octagon
(ii) a regular 20-gon
Solution:
(i) In a regular octagon, number of sides (n) = 8
∴ Each exterior angle = 360∘/8  = 45°
∴ Each interior angle = 180° – 45° = 135°

(ii) For a regular 20-gon, the number of sides (n) = 20
∴ Each exterior angle =360∘/20 = 18°
Thus, each interior angle = 180° – 18° = 162°

Try These (Page No. 47)

Question 5.
Take two identical set squares with angles 30° – 60° – 90° and place them adjacently to form a parallelogram as shown in Fig 3.20. Does this help you to verify the above property?

Solution:
The given figure helps us to verify that opposite sides of a parallelogram are of equal length.

Try These (Page No. 48)

Question 6.
Take two identical 30° – 60° – 90° set-squares and form a parallelogram as before. Does the figure obtain the help you to confirm the above property?
Solution:
The above figure also helps us to confirm that: opposite angles of a parallelogram are equal.