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 = \(\frac{360^{\circ}}{6}\) = 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 = \(\frac{360^{\circ}}{8}\) = 45°

∴ Each interior angle = 180° – 45° = 135°

(ii) For a regular 20-gon, the number of sides (n) = 20

∴ Each exterior angle = \(\frac{360^{\circ}}{20}\) = 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.