Question

The sum of all the interior angles of a polygon is four times the sum of its exterior angles .Find the number of sides in the polygon. Also ,find the measure of each exterior angle and each interior angle.

Answer 1

Answer:

10 sided polygon

Step-by-step explanation:

The sum of the interior angles of a polygon is four times the sum of its exterior angles.

The sum of the exterior angles of a polygon is always equal to 360°.  

The sum of the interior angles of polygon = 180 ( n-2 )

=> 180 ( n-2 ) = 4 × 360

=> n − 2 = 8  

=> n = 10  

Number of sides in the polygon = 10

Exterior angle = $\frac{360}{n} = \frac{360}{10} =$ 36°

Interior angle = $\frac{180(n-2)}{n} = \frac{180(10-2)}{10} = \frac{180*8}{10} =$ 18 × 8 = 144°