Q. 223.9( 7 Votes )

The sum of the interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sides of the polygon.

Answer :

The sum of interior angles of a polygon = (n – 2) × 180° …..(i)


The Sum of exterior angle of a plygon is 360°


According to the question:


Sum of interior angles = 3 × sum of exterior angles


Sum of interior angles = 3 × 360° = 1080°


Now applying relation as per equation (i)


(n – 2) × 180° = 1080°


n – 2 =


n – 2 = 6


n = 6 + 2 = 8


Therfore numbers of sides in the polygon are 8.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Smart Revision | Let's Revise Properties of PolygonSmart Revision | Let's Revise Properties of PolygonSmart Revision | Let's Revise Properties of Polygon32 mins
Smart Revision | Let's Classify Quadrilaterals and Find their PropertiesSmart Revision | Let's Classify Quadrilaterals and Find their PropertiesSmart Revision | Let's Classify Quadrilaterals and Find their Properties34 mins
NCERT I Quiz on Understanding QuadrilateralsNCERT I Quiz on Understanding QuadrilateralsNCERT I Quiz on Understanding Quadrilaterals54 mins
Genius Quiz | Understanding QuadrilateralsGenius Quiz | Understanding QuadrilateralsGenius Quiz | Understanding Quadrilaterals20 mins
Quiz | Polygon & their PropertiesQuiz | Polygon & their PropertiesQuiz | Polygon & their Properties46 mins
Members of QuadrilateralsMembers of QuadrilateralsMembers of Quadrilaterals65 mins
Smart Revision | All Types of Quadrilaterals and Their PropertiesSmart Revision | All Types of Quadrilaterals and Their PropertiesSmart Revision | All Types of Quadrilaterals and Their Properties35 mins
RD Sharma | Understanding Shapes (Polygons) Part 1RD Sharma | Understanding Shapes (Polygons) Part 1RD Sharma | Understanding Shapes (Polygons) Part 142 mins
QuadrilateralsQuadrilateralsQuadrilaterals32 mins
Quiz | Visualising Solid ShapesQuiz | Visualising Solid ShapesQuiz | Visualising Solid Shapes36 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses