Question

Let A and B be two regular polygons having a and b sides, respectively. If b = 2a and each interior angle of B is 3/2 times each interior angle of A, then each interior angle, in degrees, of a regular polygon with a + b sides is (type in box)

Answer 1

Calculation:

Each interior angle of regular polygon A = {(a – 2)180°}/a

Each interior angle of regular polygon B = {(b – 2)180°}/b

Putting b = 2a

⇒ {(2a – 2)180°}/2a

⇒ {(a – 1)180°}/a

Each interior angle of B is 3/2 times each interior angle of A

⇒ {(a – 1)180°}/a = 3/2{(a – 2)180°}/a

⇒ 2{(a – 1)180°} = 3{(a – 2)180°}

⇒ a × 360° – 360° = a × 540° – 1080° 

⇒ (540° – 360°)a = 1080° – 360°

⇒ 180°a = 720°

⇒ a = 4

Then b = 8

Regular polygon of sides (a + b) = 12

Each interior angle of a 12 sided regular polygon = {(12 – 2)180°}/12

⇒ (180° × 10)/12

⇒ 1800°/12

⇒ 150° 

∴ Each interior angle of a regular polygon with a + b sides is 150°

​​Each interior angle of a n sided regular polygon = {(n – 2)180°}/n