Question: n-sided regular polygons are arranged side-by-side to form a ring of a p-sided regular polygon.
(a) Express p in terms of n.
(b) Hence explain if a 12-sided polygon can be formed by arranging a number of regular polygons in a ring.

Please help! Answers with explanations will be marked brainliest!​

Well if you were going to think of a circle you can divide it into 4 equal sizes in one of the is equal to two pentagons and a half. If you add all is equal to a loop full of pentagons [which makes 10 pentagons]. Because the ring is made out of regular pentagons, we can work out that each of the interior angles of each pentagon is 108* degrees. By extending the lines that two pentagons share, assuming they will all meet in the middle, it will create a triangle. As we know each angle of a [regular] pentagon is 108* degrees, we know the two base angles of the triangle would equal to 72** which leaves the top angle to be 36 degrees. As [the sum of] angles at a point is 360 degrees, and 36 is divisible by 360, it will make a complete ring. Also, as 360 ÷ 36 = 10, we know that the ring will be made out of 10 pentagons. as formula to calculate the the size of a interior angle of a polygon is (n×180−360)÷n (for n being the number of sides that the polygon has). because the triangle is made by extending the lines, and angles on a line is 180 degrees, 180−108 (an interior angle of a pentagon) =72.

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