# 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 x ^{o}, (x + 20)^{o}, (x + 40)^{o}, (x + 60)^{o} and (x + 80)^{o}. The smallest angle of the pentagon is **

Ans: (b) 68^{o}

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 = 68^{o}

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

Ans: (b) 9

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

Let the number of the polygon be n.

**(8) Each interior angle of a polygon is 108 ^{o}. How many sides does it have?**

Ans: (c) 5

**(9) Each interior angle of a polygon is 135 ^{o}. 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) 144^{o}

**(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 1080 ^{o}. What is the measure of each of its interior angles?**

Ans: (a) 135^{o}

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 108 ^{o}. How many sides does the polygon have?**

Ans: (d) 10

Solution: Let the number of sides of the polygon be n.