The Sum of the Interior Angles of a Polygon is Four Times the Sum of Its Exterior Angles. Find the Number of Sides in the Polygon - Mathematics

The sum of the interior angles of a polygon is four times the sum of its exterior angles.
Find the number of sides in the polygon.

Sum

The sum of the interior angle=4 times the sum of the exterior angles.

Therefore the sum of the interior angles = 4 × 360° =1440°.

Now we have
( 2n - 4 ) x 90° = 1440°
2n - 4 = 16
2n = 20
n = 10
Thus the number of sides in the polygon is 10.

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Chapter 14 Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
Exercise 14 (A) | Q 1 | Page 168

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