For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is: A. 396 B. 324 C. 216 D. 144

GATE 2021 · General Aptitude · Patterns In Two Dimensions · medium

Answer: Each interior angle of a regular 10-sided polygon is 144 degrees — option D.

1. Write the interior angle formula: For a regular polygon with n sides, each interior angle = (n - 2) x 180 / n degrees.
2. Substitute n = 10: (10 - 2) x 180 / 10 = 8 x 180 / 10 = 1440 / 10 = 144 degrees.
3. Verify via exterior angle: Exterior angle = 360 / 10 = 36 degrees. Interior angle = 180 - 36 = 144 degrees. Confirmed.