Mensa Question - squares with shapes and lines within them

What's the next square?

It was extracted from an IQ test of Mensa. There is no trap except I don't know if it can be solved.

There's some French before the question:

Parmi les 5 figures proposées, laquelle prolonge la série ?

which translates to:

Of the 5 figures proposed, which extends the series?

The first figure has 5 sides. The second has 6 sides and 2 rows outside. Let's assume that this 2 rows are the number of sides to subtract. So the second figure would have 4 sides and the third would have 4 - 1 = 3 sides. In this sequence, we have 5, 4, 3 and expect the next number will be 2.
The answer "a" have 3 - 1 = 2 sides, so I think it's the answer.

• So the square following the answer contains a rare two-sided polygon.
– Tom
Aug 31, 2017 at 8:53

The pattern could be:

A normal figure has 5 corners. A better figure has +1 corner and a = sign in bottom right corner. A poorer figure has -1 corner and a - sign in bottom right corner.

The next figure could be

d

• Sorry, somebody change the sentence, we don't search wich one could go with the others. The real sentence is what is the next square. Aug 30, 2017 at 7:14

In the first three figures,

the total number of lines (edges of the polygon plus unattached lines in the corner) is equivalent to 2 mod 3, and all quadrilaterals are rectangles.

The only one of the options that conforms to the above is

e.

• I sit back and wait, anticipating that the other two options will be supported also. Aug 30, 2017 at 5:39
• The lines in the corner are irrelevant. What counts is the number of sides in the polygon. The sequence is: 5, 6, 4, 5, 3, 4. Therefore, the next in the series is the only five-sided figure: c. Give me a minute, and I'll see if I can come up with a rationale for b. Aug 30, 2017 at 6:42