Question

THE EXTERIOR ANGLE OF A PENTAGON ARE IN THE RATIO 1:2:3:4:5. FIND ALL THE INTERIOR ANGLES OF THE PENTAGON.

Answer 1

We know that sum of exterior angles of a regular polygon : 360°

Given exterior angles are in the ratio 1 : 2 : 3 : 4 : 5
Let the exterior angles be x, 2x, 3x, 4x and 5x

x + 2x + 3x + 4x + 5x = 360
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 : (180 - 24) , (180 - 48) , (180 - 72) , (180 - 96) and (180 - 120)
156° , 132° , 108° , 84° and 60°