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.