a pentagon with four right angles?

Question

show a picture

Answer 1

I'm pretty sure this is impossible, at least in Euclidian geometry.

Answer 2

The only thing I can think of that fits is a square, with one side "dented" inwards a bit. As long as the point of the dent is not at the center of the square, then it is not 90 degrees.

The question seems to be a bit of a trick one! It doesn't say it has to be a REGULAR pentagon (one where all sides are the same length and all angles are equal).

The second part is that for polygons with more than 4 sides, you usually say that all the EXTERNAL angles add up to 360 degrees. I think this is the second part of the trick - You have to count the external angles in this as well as the internal ones.

The two corners of the square have internal angles of 90 degrees of course, but also external angles of 90 degrees as well. So this pentagon has four right angles, as long as the corner of the dent isn't 90 degrees as well!

There are slight variations on it, say with the dented side coming out, instead of going in, or with both sides of the dent being the same size (or different sizes), or even using a rectangle instead of a square. All boil down to the same sort of solution though.

I hope this helps a bit?!

Answer 3

It is not possible for a pentagon on a flat surface to contain four right-angles unless you draw a square and argue that one of the sides contains the remaining vertex with an interior angle of 180 degrees.

Answer 4

maybe on a spherical plane or with concave pentagon

Answer 5

There are 5 vertex

if you draw a line from one vertex and continue until all five vertex are complete. you will have 5 obtuse Triangles

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Answer 6

Its not possible. It would be a square then.