We know the sum of the interior angles of a triangle is 180°. Show that the sums of the interior angles of polygons with 3, 4, 5, 6, … sides form an arithmetic progression. Find the sum of the interior angles for a 21-sided polygon
Given the sum of interior angles of a polygon having ‘n’ sides is given by (n – 2) × 180°
Sum of angles with three sides that is n = 3 is (3 – 2) × 180° = 180°
Sum of angles with four sides that is n = 4 is (4 – 2) × 180° = 360°
Sum of angles with five sides that is n = 5 is (5 – 2) × 180° = 540°
Sum of angles with six sides that is n = 6 is (6 – 2) × 180° = 720°
As seen as the number of sides increases by 1 the sum of interior angles increases by 180°
Hence the sequence of sum of angles as number of sides’ increases is 180°, 360°, 540°, 720° …
The sequence is AP with first term as a = 180° and common difference as d = 180°
We have to find sum of angles of polygon with 21 sides
Using (n – 2) × 180°
⇒ Sum of angles of polygon having 21 sides = (21 – 2) × 180°
⇒ Sum of angles of polygon having 21 sides = 19 × 180°
⇒ Sum of angles of polygon having 21 sides = 3420°
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,