Premium Online Home Tutors

3 Tutor System

Starting just at 265/hour

What can you say about the angle sum of a convex polygon with number of sides?

(a) 7

(b) 8

(c) 10

(d) n

Answer :

From the given table, dearly we observe that the sum of angles (interior angles) of a polygon with n sides = \((n – 2)× 180^{\circ}\).

(a) n = 7

Sum of angle =\(\left( 7-2 \right) \times { 180 }^{ \circ }\)

\(= 5\times { 180 }^{ \circ }={ 900 }^{ \circ }\)

∴The sum of angle for 7 sided polygon=\(900^o\)

(b) n = 8

Sum of angles =\( \left( 8-2 \right) \times { 180 }^{ \circ }\)
\(= 6\times { 180 }^{ \circ }={ 1080 }^{ \circ }\)

∴ The sum of the angles of a polygon of 8 sides=\(1080^o\)

(c) n = 10

Angle sum = \(\left( 10-2 \right) \times { 180 }^{ \circ }\)

\(= 8\times { 180 }^{ \circ }={ 1440 }^{ \circ }\)

∴ The sum of the angles of a polygon of 10 sides=\(1440^o\)

(d) We can observe from the given table that the number of triangles is two less them the number of sides in the polygon.

∴ If the polygon has n sides, the number of triangles formed will be (n – 2).

Also we know that the sum of angles of a triangle = \(180^{ \circ }\)

∴ The sum of angles of a polygon of n sides =\( (n – 2) \times180^{ \circ }\)

- 1. Given here are some figures : Classify each of them on the basis of the following : (a) Simple curve (b) Simple closed curve (c) Polygon (d) Convex polygon (e) Concave polygon
- 2.How many diagonals does each of the following have? (a) A convex quadrilateral (b) A regular hexagon (c) A triangle.
- 3.What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and j try!)
- 5.What is a regular polygon? State the name of a regular polygon of (i) 3 slides (ii) 4 slides (iii) 6 slides
- 6.Find the angle measure x in the following figures.
- 7. (a) Find x + y + z (b) Find x + y + z + w

- 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