CG Board Class 8 Mathematics Chapter 10 Solutions: Polygon (बहुभुज) – 2026-27

(i) a parallelogram (ii) quadrilateral (iii) rectangle (iv) trapezium**

(i) parallelogram (ii) trapezium (iii) rectangle (iv) rhombus

(i) 60°(ii) 120°(iii) 90°(iv) 180°

(i) 14 cm (ii) 28 cm (iii) 56 cm (iv) 60 cm

(1) A quadrilateral where the diagonals are equal and intersect each other at right angle, is known as a ……………….**

• (2) The quadrilateral in which only one pair of opposite sides are parallel is known as an ……………….
• (3) If a polygon has 6 vertices, then the number of sides in the polygon would be ………
• (4) If the number of sides in a polygon is “n” then the number of diagonals that can be drawn from one of the vertices would be ……………….

Cutting off the 4 vertices (corners) of a square adds 4 new straight edge segments to the existing 4 sides, resulting in an 8-sided polygon called an Octagon.

Sum of internal angles = (n – 2) × 180°.

Here n = 8.

Sum of internal angles = (8 – 2) × 180°= 6 × 180°= 1080°(अंतःकोणों का योग = (8 – 2) × 180°= 1080°।)

• Let the given angle be ∠ A = 120°.
• Opposite angle ∠ C = ∠ A = 120°(opposite angles of a parallelogram are equal).
• Adjacent angle ∠ B = 180°- 120°= 60°(adjacent angles are supplementary).
• Opposite angle ∠ D = ∠ B = 60°.
• (समान्तर चतुर्भुज के सम्मुख कोण बराबर तथा आसन्न कोण संपूरक होते हैं।)

The remaining angles are 120°, 60°, 60°.

• Let the adjacent sides be 3x and 4x.
• Perimeter formula = 2 × (3x + 4x) = 14x.
• Given Perimeter = 84 cm.

14x = 84 ⇒ x = 84/14 = 6

• First side = 3 × 6 = 18 cm.
• Second side = 4 × 6 = 24 cm.
• (पहली भुजा = 18 सेमी, दूसरी भुजा = 24 सेमी।)

1. All squares are rhombus. (सभी वर्ग समचतुर्भुज होते हैं।)

सत्य.

1. The diagonals of a rectangle are equal. (आयत के विकर्ण समान होते हैं।)

सत्य.

1. All rectangles are not parallelograms. (सभी आयत समान्तर चतुर्भुज नहीं होते हैं।)

असत्य.

• Correction / संशोधन: All rectangles are parallelograms. (सभी आयत समान्तर चतुर्भुज होते हैं।)

1. The diagonals of a parallelogram bisect each other at right angles. (समान्तर चतुर्भुज के विकर्ण एक-दूसरे को समकोण पर समद्विभाजित करते हैं।)

असत्य.

• Correction / संशोधन: The diagonals of a parallelogram bisect each other, but not necessarily at right angles. (समान्तर चतुर्भुज के विकर्ण एक-दूसरे को समद्विभाजित करते हैं, परंतु सदैव समकोण पर नहीं।)

1. All squares are rectangles. (सभी वर्ग आयत होते हैं।)

सत्य.

### EXERCISE 10.2 (प्रश्नावली 10.2)

• Sum of all interior angles of a quadrilateral = 360°.
• Let fourth angle = x.

80°+ 110°+ 120°+ x = 360°310°+ x = 360°x = 360°- 310°= 50°

• Let each of the three equal angles = x.

x + x + x + 75°= 360°3x + 75°= 360°3x = 360°- 75°= 285°x = frac{285°{3} = 95°

• Let adjacent angles be 2x and 3x.
• Sum of adjacent angles of a parallelogram = 180°.

2x + 3x = 180° ⇒ 5x = 180° ⇒ x = 36°* First angle = 2 × 36°= 72°.

• Second angle = 3 × 36°= 108°.
• Opposite angles are equal, so the four angles are 72°, 108°, 72°, 108°.

• Right angle = 90°.
• Let the remaining angles be 2x, 3x, 4x.

90°+ 2x + 3x + 4x = 360°9x = 360°- 90°= 270° ⇒ x = 30°* First remaining angle = 2 × 30°= 60°.

• Second remaining angle = 3 × 30°= 90°.
• Third remaining angle = 4 × 30°= 120°.

• Let the angles be 1x, 2x, 3x, 4x.

1x + 2x + 3x + 4x = 360°10x = 360° ⇒ x = 36°* Angles are:

• 1 × 36°= 36° 2 × 36°= 72° 3 × 36°= 108°* 4 × 36°= 144°

• Sum of adjacent angles = 180°.

x + (x + 20) = 180°2x + 20 = 180° ⇒ 2x = 160° ⇒ x = 80°* First angle = 80°.

• Second angle = 80°+ 20°= 100°.
• Opposite angles are equal, so the four angles are 80°, 100°, 80°, 100°.