Question

the exterior angles of a Pentagon are in the ratio 1 : 2 : 3 : 4 : 5. Find all the interior angles of the Pentagon? Someone plz give me this answer with solution. Thanks

Answer 1

We know , sum of exterior angles of a regular polygon : 360°
Let the angles be x,2x,3x,4x and 5x
15x = 360°
x = 24
So , exterior angles : 24°,48°,72°,96° and 120°
Now , we know an exterior and its corresponding interior angles sum up to 180°
So , correspondence interior angles will be obtained by subtracting these exterior angles from 180°
Interior angles of Pentagon : 156°,132°,108°,84° and 60°

Answer 2

Let it be x.

We know that sum of all exterior angles = 360

Given, x + 2x + 3x + 4x + 5x = 360

             15x = 360

               x = 24.

The angles will be 24,48,72,96,120.

Interior angles will be (180-24),(180-48),(180-72),(180-96),(180-120)

                                    = 156,132,108,84,60.


Hope this helps!