# RS Aggarwal Class 8 Math Fourteenth Chapter Polygons Exercise 14B Solution

## EXERCISE 14B

### OBJECTIVE QUESTIONS

#### Tick (√) the correct answer in each of the following:

(1) How many diagonals are there in a pentagon?

Ans: (a) 5 (2) How many diagonals are there in a hexagon?

Ans: (c) 9 (3) How many diagonals are there in an octagon?

Ans: (d) 20 (4) How many diagonals are there in a polygon having 12 sides?

Ans: (d) 54 (5) A polygon has 27 diagonals. How many sides does it have?

Ans: (c) 9

Solution: Let the number of side of the polygon be n. Hence, number of the sides can’t be negative. So,

∴ n – 9 = 0

⇒ n = 9

(6) The angles of a pentagon are xo, (x + 20)o, (x + 40)o, (x + 60)o and (x + 80)o. The smallest angle of the pentagon is

Ans: (b) 68o

Solution: We know, sum of interior angles = (2n – 4) right ∠s.

= (10 – 4) × 90 = 540

∴ x + x + 20 + x + 40 + x + 60 + x + 80 = 540

⇒ 5x + 200 = 540

⇒ 5x = 540 – 200

⇒ 5x = 340

⇒ x = 68o

(7) The measure of each exterior angle of a polygon is 40o. How many sides does it have?

Ans: (b) 9

Solution: We know, sum of all exterior angles = 4 right ∠s = 360o

Let the number of the polygon be n. (8) Each interior angle of a polygon is 108o. How many sides does it have?

Ans: (c) 5 (9) Each interior angle of a polygon is 135o. How many sides does it have?

Ans: (a) 8 ⇒ 45n = 360

⇒ n = 8

(10) In a regular polygon, each interior angle is thrice the exterior angle. The number of sides of the polygon is

Ans: (b) 8

Solution: Let the number of sides of the polygon be n. (11) Each interior angle of a regular decagon is

Ans: (c) 144o (12) The sum of all interior angles of a hexagon is

Ans: (b) 8 right angle ∠s

Solution: Sum of all interior angles of a hexagon = (12 – 4) right ∠s = 8 right ∠s.

(13) The sum of all interior angles of a regular polygon is 1080o. What is the measure of each of its interior angles?

Ans: (a) 135o

Solution: Sum of all interior angles of a regular polygon = (2n – 4) right ∠s

Let the number of sides of the regular polygon be n. (14) The interior angle of a regular polygon exceeds its exterior angle by 108o. How many sides does the polygon have?

Ans: (d) 10

Solution: Let the number of sides of the polygon be n. Updated: May 30, 2022 — 2:31 pm