A1 and A2 are two regular polygons. The sum of all the interior angles of A1 is 1080º. Each interior angle A2 exceeds its exterior angle by 132º. The sum of the number of sides A1 and A2 is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 23.
The sum of all the interior angle of side n = (n - 2) × 180
(n - 2) × 180 = 1080
n = 8
Number of sides of A1 polygon = 8.
For A2 ,
interior angle = 132 + Exterior angle.
Let the exterior angle be x then interior angle = 132 + x.
We know that, Exterior angle + interior angle of the same exterior angle = 180 ( linear pair)
x + 132 + x = 180
2x = 48
x = 24.
Number of sides of A2 = 360/24 = 15
Required sum = 15 + 8 = 23.