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Ex 3.2, 4 - How many sides does a regular polygon have if interior

Ex 3.2, 4 - Chapter 3 Class 8 Understanding Quadrilaterals - Part 2
Ex 3.2, 4 - Chapter 3 Class 8 Understanding Quadrilaterals - Part 3


Transcript

Ex 3.2, 4 (Introduction) How many sides does a regular polygon have if each of its interior angles is 165°?Let there be a triangle ∆ ABC where ∠ A = 22° Let ∠ 1 be the exterior angle Since BAD is a line ∠ BAC + ∠1 = 180° ∠ 1 = 180° − 22° ∠ 1 = 158° So, in a polygon Interior angle + Exterior angle = 180° Ex 3.2, 4 How many sides does a regular polygon have if each of its interior angles is 165°?Given Interior angle = 165° Now, By linear pair Interior angle + Exterior angle = 180° 165° + Exterior angle = 180° Exterior angle = 180° − 165° = 15° Let number of sides = n In a regular Polygon Sum of the exterior angles = 360° Exterior Angle × Number of sides = 360° 15° × n = 360° n = 360"°" /15"°" n = 24 ∴ Polygon has 24 sides

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.