Let A and B be two regular polygons having a and b sides, respectively. If b = 2a and each interior angle of B is times each interior angle of A, then each interior angle, in degrees, of a regular polygon with a + b sides isCorrect answer is '150'. Can you explain this answer?

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Let A and B be two regular polygons having a and b sides, respectively. If b = 2a and each interior angle of B is

times each interior angle of A, then each interior angle, in degrees, of a regular polygon with a + b sides is

Correct answer is '150'. Can you explain this answer?

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Let A and B be two regular polygons having a and b sides, respectively...

Each interior angle in an n-sided polygon = (n - 2)180 / n
It is given that each interior angle of B is times each interior angle of A and b = 2a
(b - 2)180 / b = 3 / 2 x (a - 2)180 / a
2 x (b - 2) x a = 3 x (a - 2) x b
2(ab - 2a) = 3(ab - 2b)
ab - 6b + 4a = 0
a * 2a - 12a + 4a = 0
2a² - 8a = 0
a(2a - 8) = 0
a cannot be zero so 2a=8
a=4, b = 4*2=8
a+b = 12
Each interior angle of a regular polygon with 12 sides = (12 - 2) x 180 / 12
= 150

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Let A and B be two regular polygons having a and b sides, respectively. If b = 2a and each interior angle of B is times each interior angle of A, then each interior angle, in degrees, of a regular polygon with a + b sides isCorrect answer is '150'. Can you explain this answer?

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