Lesson: Polygons

No. If the question doesn't stated that the polygon is regular, we can't assume that it's regular.

Question link: https://greprepclub.com/forum/length-of-a-side-of-regular-pentagon-with-...

Good question.
The word "regular" tells us that all sides are equal.
Without the word "regular," we wouldn't be able to make any conclusions about the lengths of the sides.

Cheers,
Brent

That's correct; the 4 angles in a quadrilateral will ALWAYS add to 360°.
So, to answer your second question, the angles in a quadrilateral CANNOT have a sum less than 180°.

Where do I say that the angles in a quadrilateral have a sum less than 180°?

Cheers,
Brent

Question link: https://greprepclub.com/forum/given-figure-is-that-of-a-regular-hexagon-...

The 6 angles in a hexagon will add to 720 degrees.

In the my solution to the above question, I divide the regular hexagon into 6 equilateral triangles.

Notice that each equilateral triangle has one of its angles at the CENTER of the hexagon.
These six angles at the CENTER are not part of the angles in a hexagon. So, we can disregard them.
When we disregard them, we see that the angles add to 720 degrees.

Does that help?

Cheers,
Brent

Absolutely! The perimeter of a polygon inscribed in a circle will always be less than the circumference of the inscribing circle.

Question link: https://greprepclub.com/forum/in-a-particular-seven-sided-polygon-the-su...

Your approach yielded the correct answer, but it's not valid.
If each of the four angles were 225, then the other three angles would be 0 degrees (which is impossible)

Cheers,
Brent

Question link: https://greprepclub.com/forum/what-is-the-area-of-the-figure-below-11775...

That's a perfectly valid approach. Nice work!