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Question 11 : 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 [TITA]


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Explanatory Answer

Sum of the interior angles of a n-sided Polygon = (n-2) x 180
Measure of each interior angle =
So, Interior angle of the polygon with side a =
Interior angle of the polygon with side b =
It is given that interior angle of side b is 3/2 times to that of the polygon with side A
= x
(2a-2) x 180 = (3a - 6) x 180
2a - 2 = 3a - 6
a = 4
So, b = 8
(a + b) sides = 8 + 4 = 12 sides
Interior angle = = 150o


The question is "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 [TITA] "

Hence, the answer is 150

 

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