Rs Aggarwal 2018 Solutions for Class 8 Math Chapter 14 Polygons are provided here with simple step-by-step explanations. These solutions for Polygons are extremely popular among Class 8 students for Math Polygons Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2018 Book of Class 8 Math Chapter 14 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2018 Solutions. All Rs Aggarwal 2018 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.
Page No 182:
Question 1:
Find the measure of each exterior angle of a regular
(i) pentagon
(ii) hexagon
(iii) heptagon
(iv) decagon
(v) polygon of 15 sides.
Answer:
Exterior angle of an n-sided polygon =
(i) For a pentagon:
(ii) For a hexagon:
(iii) For a heptagon:
(iv) For a decagon:
(v) For a polygon of 15 sides:
Page No 182:
Question 2:
Is it possible to have a regular polygon each of whose exterior angles is 50°?
Answer:
Each exterior angle of an n-sided polygon =
If the exterior angle is 50°, then:
Since n is not an integer, we cannot have a polygon with each exterior angle equal to 50°.
Page No 182:
Question 3:
Find the measure of each interior angle of a regular polygon having
(i) 10 sides
(ii) 15 sides.
Answer:
For a regular polygon with n sides:
(i) For a polygon with 10 sides:
(ii) For a polygon with 15 sides:
Page No 182:
Question 4:
Is it possible to have a regular polygon each of whose interior angles is 100°?
Answer:
Each interior angle of a regular polygon having n sides =
If each interior angle of the polygon is 100°, then:
Since n is not an integer, it is not possible to have a regular polygon with each interior angle equal to 100°.
Page No 182:
Question 5:
What is the sum of all interior angles of a regular
(i) pentagon
(ii) hexagon
(iii) nonagon
(iv) polygon of 12 sides?
Answer:
Sum of the interior angles of an n-sided polygon =
(i) For a pentagon:
(ii) For a hexagon:
(iii) For a nonagon:
(iv) For a polygon of 12 sides:
Page No 182:
Question 6:
What is the number of diagonals in a
(i) heptagon
(ii) octagon
(iii) polygon of 12 sides?
Answer:
Number of diagonal in an n-sided polygon =
(i) For a heptagon:
(ii) For an octagon:
(iii) For a 12-sided polygon:
Page No 182:
Question 7:
Find the number of sides of a regular polygon whose each exterior angle measures:
(i) 40°
(ii) 36°
(iii) 72°
(iv) 30°
Answer:
Sum of all the exterior angles of a regular polygon is .
(i)
(ii)
(iii)
(iv)
Page No 182:
Question 8:
In the given figure, find the angle measure x.
Answer:
Sum of all the interior angles of an n-sided polygon =
∴ x = 105
Page No 182:
Question 9:
Find the angle measure x in the given figure.
Answer:
For a regular n-sided polygon:
Each interior angle =
In the given figure:
∴ x = 108
Page No 182:
Question 1:
Tick (✓) the correct answer:
How many diagonals are there in a pentagon?
(a) 5
(b) 7
(c) 6
(d) 10
Answer:
(a) 5
For a pentagon:
Page No 182:
Question 2:
Tick (✓) the correct answer:
How many diagonals are there in a hexagon?
(a) 6
(b) 8
(c) 9
(d) 10
Answer:
(c) 9
Number of diagonals in an n-sided polygon =
For a hexagon:
Page No 182:
Question 3:
Tick (✓) the correct answer:
How many diagonals are there in an octagon?
(a) 8
(b) 16
(c) 18
(d) 20
Answer:
(d) 20
For a regular n-sided polygon:
Number of diagonals =:
For an octagon:
Page No 182:
Question 4:
Tick (✓) the correct answer:
How many diagonals are there in a polygon having 12 sides?
(a) 12
(b) 24
(c) 36
(d) 54
Answer:
(d) 54
For an n-sided polygon:
Number of diagonals =
Page No 182:
Question 5:
Tick (✓) the correct answer:
A polygon has 27 diagonals. How many sides does it have?
(a) 7
(b) 8
(c) 9
(d) 12
Answer:
(c) 9
Page No 183:
Question 6:
Tick (✓) the correct answer:
The angles of a pentagon are x°, (x + 20)°, (x + 40)°, (x + 60)° and (x + 80)°. The smallest angle of the pentagon is
(a) 75°
(b) 68°
(c) 78°
(d) 85°
Answer:
(b) 68°
Sum of all the interior angles of a polygon with n sides =
Page No 183:
Question 7:
Tick (✓) the correct answer:
The measure of each exterior angle of a regular polygon is 40°. How many sides does it have?
(a) 8
(b) 9
(c) 6
(d) 10
Answer:
(b) 9
Page No 183:
Question 8:
Tick (✓) the correct answer:
Each interior angle of a polygon is 108°. How many sides does it have?
(a) 8
(b) 6
(c) 5
(d) 7
Answer:
(c) 5
Each interior angle for a regular n-sided polygon =
Page No 183:
Question 9:
Tick (✓) the correct answer:
Each interior angle of a polygon is 135°. How many sides does it have?
(a) 8
(b) 7
(c) 6
(d) 10
Answer:
(a) 8
Page No 183:
Question 10:
Tick (✓) the correct answer:
In a regular polygon, each interior angle is thrice the exterior angle. The number os sides of the polygon is
(a) 6
(b) 8
(c) 10
(d) 12
Answer:
(b) 8
For a regular polygon with n sides:
Each exterior angle =
Each interior angle =
Page No 183:
Question 11:
Tick (✓) the correct answer:
Each interior angle of a regular decagon is
(a) 60°
(b) 120°
(c) 144°
(d) 180°
Answer:
(c) 144°
Each interior angle of a regular decagon =
Page No 183:
Question 12:
Tick (✓) the correct answer:
The sum of all interior angles of a hexagon is
(a) 6 right ∠s
(b) 8 right ∠s
(c) 9 right ∠s
(d) 12 right ∠s
Answer:
(b)
Sum of all the interior angles of a hexagon is right angles.
For a hexagon:
Page No 183:
Question 13:
Tick (✓) the correct answer:
The sum of all interior angles of a regular polygon is 1080°. What is the measure of each of its interior angles?
(a) 135°
(b) 120°
(c) 156°
(d) 144°
Answer:
(a) 135°
Page No 183:
Question 14:
Tick (✓) the correct answer:
The interior angle of a regular polygon exceeds its exterior angle by 108°. How many sides does the polygon have?
(a) 16
(b) 14
(c) 12
(d) 10
Answer:
(d) 10
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