Question

Select one of the following four options that will make the 2nd pair analogous to the 1st pair given.
Hexagon : 9 :: Decagon :?

• A. 50
• B. 45
• C. 40
• D. 35

Answer 1

The Correct Option is D

A Hexagon has 6 sides, and the sum of the interior angles of a polygon is given by the formula: (n − 2) ×180◦, where n is the number of sides. For a Hexagon, this results in 2 (6 −2)×180 = 720◦. If we divide 720 by 20 (the number of equal angles in the Hexagon), we get 36°. Similarly, for the Decagon (10 sides), the sum of interior angles is (10 −2)×180 = 1440◦, which when divided by 40 gives 36°. Therefore, the analogous answer is 35, as it keeps the angle-per-side relationship consistent.

Conclusion: The correct answer is 35, as it maintains the balance of angles in polygons, especially the Decagon.