Question

The sum of the measures of the interior angles is 1.440 degrees. How many sides does the polygon have?

Answer 1

Number of sides of polygon = N =10

Explanation:

Given as , the sum of measures of the interior angles = 144 degree

Let the number of sides = N

Now, External angle =
`(360)/(N)`

And Interior angle = 180° - Exterior angles

Or, Interior angle = 180° -
`(360°)/(N)`

Or , 144° = 180° -
`(360°)/(N)`

Or,
`(360°)/(N)` = 180° - 144°

Or ,
`(360°)/(N)` = 36°

∴ N =
`(360°)/(36°)`

Hence, Number of sides of the polygon = 10 Answer