Each side of polygon is parallel to either the X or...

LUANDATO wrote:Each side of polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90° or concave if the internal angle is 270°. If the number of convex corners in such a polygon is 25, the number of concave corners must be:

(A) 20
(B) 0
(C) 21
(D) 22
(E) 23

The OA is C.

I'm really confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

Sum of all the angles of a polygon = 180(n – 2); where n = number of sides of the polygon

Let the total number of convex angle (90º) be x and the total number of concave angle (270º) be y

=> n = x + y

Sum of all the angles of a polygon = 180(x + y – 2)

90x + 270y = 180(x + y – 2)
90x + 270y = 180x + 180y – 360
90y = 90x –360

Given that x = 25
=> y = (90*25 – 360)/90
y = 21

The correct answer: [spoiler][/spoiler]

Hope this helps!

-Jay
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