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

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 what is the measure of each interior angle, in degrees, of a regular polygon with a + b sides?

A. 100
B. 120
C. 150
D. 160
E. 170

Are You Up For the Challenge: 700 Level Questions

A. 100
B. 120
C. 150
D. 160
E. 170

Are You Up For the Challenge: 700 Level Questions

GMATinsight · Answer

Bunuel

Is the highlighted part correct???

I think that a should be the Number of sides of polygon A instead length of the side

yashikaaggarwal · Answer

As per the question, if we consider the interior angle of B as 3/2 of angle A. Which gives B as a five side polygon and A as a square. But adding up the sides is not giving the following options as answer. Please elaborate the question. I might be getting it all wrong.
Thank you in advance.

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Bunuel · Answer

Yes, you are right. Edited. Thank you.

Archit3110 · Answer

interior angle of a polygon = (n-2)*180/n
given b=3/2 *a and sides are b=2a
we have
use (n-2)*180/n
so we have
(b-2)*180/b = 3/2* ( a-2)*180/a
put b=2a
we get
2a-2*180/2a = 3/2 * (a-2) *180/a
solve a= 4 and b = 8
total sides a+b= 12
angle measure of 12 sided ; (12-2) *180/12 =150
OPTION C

Kinshook · Answer

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

Asked: If b = 2a and each interior angle of B is 3/2 times each interior angle of A, then what is the measure of each interior angle, in degrees, of a regular polygon with a + b sides?

Interior angle of a regular polygon  = \frac{180 (n-2)}{n} ; where n = number of sides of the regular polygon

Interior angle of a regular polygon of sides a  =180 \frac{(a-2)}{a}

Interior angle of a regular polygon of sides b = 2a  = \frac{180 (2a-2)}{2a} = \frac{180(a-1)}{a}

Since {(a-1)/a}{(a-2)/a)} = 3/2
(a-1)/(a-2) = 3/2
a = 4
b = 2a = 8
a+b = 4+8 = 12

Interior angle of a regular polygon of sides (a+b =12)= 180 (12-2)/12 = 150

IMO C

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

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

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