Premium Online Home Tutors

3 Tutor System

Starting just at 265/hour

(b) Can it be an interior angle of a regular polygon? Why?

Answer :

(a) We have, Number of sides of regular polygon=\(\frac{360^{\circ} }{Exterior \;angle}\)

As we know number of sides by the formula should be an integer so, it is not possible that a regular polygon have its exterior angle of \(22^{\circ}\) because \(22^{\circ}\) is not divisible by \(360^{\circ}\) hence, we can't get a whole number for calculating the number of side.

(b) If interior angle =\(22^{\circ}\)

And we have: measure of each interior angle=\(\frac{(n-2)\times180^o}n\)

\(\Rightarrow 180n -2 \times 180=22n\)

\(\Rightarrow 180n -22n=360\)

\(\Rightarrow 158n=360\)

\(\Rightarrow n=\frac{360}{158}\)

But 158 does not divide 360 exactly.So, the polygon is not possible.

- 1.Find x in the following figures.
- 2.Find the measure of each exterior angle of a regular polygon of (i) 9 sides (ii) 15 sides
- 3.How many sides does a regular polygon have if the measure of an exterior angle is \(24^{\circ}\)?
- 4.How many sides does a regular polygon have if each of its interior angles is \(165^{\circ}\)?
- 6.(a) What is the minimum interior angle possible for a regular polygon? Why? (b) What is the maximum exterior angle possible for a regular polygon?

- NCERT solutions for class 8 maths chapter 1 Factorisation and Mensuration
- NCERT solutions for class 8 maths chapter 1 Rational Numbers
- NCERT solutions for class 8 maths chapter 1 Factorization
- NCERT solutions for class 8 maths chapter 2 Linear Equations in One Variable
- NCERT solutions for class 8 maths chapter 3 Understanding Quadrilaterals
- NCERT solutions for class 8 maths chapter 4 Practical Geometry
- NCERT solutions for class 8 maths chapter 5 Data Handling
- NCERT solutions for class 8 maths chapter 6 Squares and Square Roots
- NCERT solutions for class 8 maths chapter 7 Cube and Cube Roots
- NCERT solutions for class 8 maths chapter 8 Comparing Quantities
- NCERT solutions for class 8 maths chapter 9 Algebraic Expressions and Identities
- NCERT solutions for class 8 maths chapter 10 Visualising Solid Shapes
- NCERT solutions for class 8 maths chapter 11 Mensuration
- NCERT solutions for class 8 maths chapter 12 Exponents and Powers
- NCERT solutions for class 8 maths chapter 13 Direct and Inverse Proportions
- NCERT solutions for class 8 maths chapter 14 Factorization
- NCERT solutions for class 8 maths chapter 15 Introduction to Graphs
- NCERT solutions for class 8 maths chapter 16 Playing with Numbers

- NCERT solutions for class 8 science chapter 1 Crop Production & Management
- NCERT solutions for class 8 science chapter 2 Microorganisms: Friend and Foe
- NCERT solutions for class 8 science chapter 3 Synthetic Fibers and Plastics
- NCERT solutions for class 8 science chapter 4 Materials: Metals and Nonmetals
- NCERT solutions for class 8 science chapter 5 Coal and Petroleum
- NCERT solutions for class 8 science chapter 6 Combustion and Flame
- NCERT solutions for class 8 science chapter 7 Conservation of Plants and Animals
- NCERT solutions for class 8 science chapter 8 Cell-Structure and Function
- NCERT solutions for class 8 science chapter 9 Reproduction in Animals
- NCERT solutions for class 8 science chapter 10 Reaching the Age of Adolsence
- NCERT solutions for class 8 science chapter 11 Force and Pressure
- NCERT solutions for class 8 science chapter 12 Friction
- NCERT solutions for class 8 science chapter 13 sound
- NCERT solutions for class 8 science chapter 14 Chemical Effects of Electric Current
- NCERT solutions for class 8 science chapter 15 Some Natural Phenomena
- NCERT solutions for class 8 science chapter 16 Light
- NCERT solutions for class 8 science chapter 17 Stars and the Solar System
- NCERT solutions for class 8 science chapter 18 Pollution of Air and Water