A₁ and A₂ are two regular polygons. The sum of all the interior angles of A₁ is 1080°. Each interior angle of A₂ exceeds its exterior angle by 132°. The sum of the number of sides A₁ and A₂ is:

Solution (By Examveda Team)

A₁ and A₂ are 2 regular polygon
Sum of internal angle of A₁ = 1080°
(n - 2) × 180° = 1080°
(n - 2) = 6
n = 6 + 2 = 8
Internal angle of each A₂ is grater than exterior angle by 132°
I + E = 180°
I - E = 132°
2I = 312°
I = 156°
E = 24°
n $$ = \frac{{{{360}^ \circ }}}{{{\text{Each Angle}}}} = \frac{{{{360}^ \circ }}}{{{{24}^ \circ }}} = 15$$
Sum of side of A₁ and A₂ = 15 + 8 = 23