You can Download KSEEB Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals InText Questions Questions and Answers helps you to revise the complete syllabus.

## KSEEB Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals InText Questions

Try These (Page 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:

Since ∠a + ∠r = 180° (CE they form a linear pair)

Hence,

(∠a + ∠r) + (∠a + ∠x) + (∠a + ∠y) + (∠a + ∠z) + (∠a + ∠p) + (∠a + ∠q) = 180° × 6

⇒ ∠a + ∠a + ∠a + ∠a + ∠a + ∠a + ∠r + ∠x + ∠y + ∠z + ∠p + ∠q = 1080°

⇒ 6∠a + ∠r + ∠x + ∠y + ∠z + ∠p + ∠q = 1080°

⇒ 6 × 120° + ∠r + ∠x + ∠y + ∠z + ∠p + ∠q = 1080°

(∵ Interior angle of a regular hexagon is 120°)

⇒ 720° + ∠r + ∠x + ∠y + ∠z + ∠p + ∠q = 1080°

⇒ ∠r + ∠x + ∠y + ∠z + ∠p + ∠q = 1080° – 720°

⇒ ∠r + ∠x + ∠y + ∠z + ∠p + ∠q = 360°

Question 2.

Is x = y = z = p = q = r? Why?

Solution:

Yes these are equal

∠x + ∠a = ∠y + ∠a = ∠z + ∠a = ∠p + ∠a = ∠q + ∠a = 180° (Linear pair)

⇒ ∠x + ∠a = 180°

⇒ ∠x + 120° = 180°

⇒ ∠x = 180° – 120°

∴ ∠x = 60°

Similarly, ∠y = ∠z = ∠p = ∠q = 60°

Question 3.

What is the measure of each?

(i) exterior angle

(ii) interior angle

Solution:

(i) The measure of each exterior angle = \(\frac{360^{\circ}}{6}\) = 60°

(ii) The measure of each interior angle = a + 60° = 180°

∴ a = 120°

Question 4.

Repeat this activity for the cases of

(i) a regular octagon

(ii) a regular 20-gon

Solution:

(i) The exterior angle of a regular octagon = \(\frac{360^{\circ}}{8}\) = 45°

The interior angle of a regular octagon = 180° – 45° = 135°

(ii) The exterior angle of a regular 20-gon = \(\frac{360^{\circ}}{20}\) = 18°

The interior angle of a regular 20-gon = 180° – 18° = 162°

Try These (Page 47)

Question 1.

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

Solution:

Yes, it helps us to verify one of the properties of a parallelogram, that its opposite sides are equal.

Try These (Page 48)

Question 1.

Take two identical 30° – 60° – 90° set squares and form a parallelogram as before. Does the figure obtain help to confirm the property (The opposite angles of a parallelogram are of equal measure)?

Solution:

Yes, it confirms the property of a parallelogram that its opposite angles are of equal measure. Here, opposite angles are 90° each.