[b]Theorem[/b]: For any integer [i]p[/i]>0 and angle measure [i]x[/i] in [math]\left(0,\frac{\left(p-2\right)\pi}{p}\right)[/math], there is a regular polygon with [i]p[/i] vertices and interior angle equal to [i]x[/i].[br][br][b]Theorem[/b]: The interior angle of a regular polygon depends on the radius of its circumcircle and vice versa.[br][br]No proofs, however explore the following 3 examples which illustrate these theorems. [br][br][b]Example 1[/b]: Adjust A, B, E and G to observe different congruent equilateral triangles. Observe that that:[br][list][*]The triangles remain congruent[/*][*]The interior angle measure depends on the radius of the circumcircle[/*][/list][br]Can you set A and B so that triangle BCD will tesselate?

[b]Example 2[/b]: Adjust A, B, F and G to observe different congruent equilateral quadrilaterals. Observe that that (like above):[br][list][*]The quadrilaterals remain congruent[/*][*]The interior angle measure depends on the radius of the circumcircle[/*][/list]Can you adjust A and B so that quadrilateral BCDE will tesselate?

[b]Example 3[/b]: Adjust A, B, G and H to observe different congruent equilateral pentagons. Observe that that (like above):[br][list][*]The pentagons remain congruent[/*][*]The interior angle measure depends on the radius of the circumcircle[/*][/list]Can you adjust A and B so that pentagon BCDEF will tesselate?