Star Study - 10 pointed individual

$join\quad all\quad points\quad to\quad form\quad a\quad circle\quad \\ Now\quad concider\quad one\quad internal\quad angle\\ the\quad arc\quad which\quad subtend\quad it.\\ In\quad total\quad there\quad are\quad 5\quad of\quad this\quad arc,joined\quad end\quad to\quad end\\ which\quad will\quad subtend\quad a\quad total\quad of\quad 360\quad in\quad centre\\ So{ \quad 72 }^{ 0 }\quad subtended\quad by\quad one\quad arc\quad in\quad centre,\\ So\quad angle\quad at\quad circumference=72/2=\quad 36\quad degree=\quad internal\quad angle=36\quad degree$

since sum of all the internal angles is 360

for each angle we have

360/10=36 .

It's actually not that complicated. If you look carefully, you can see that the drawing is just two stars drawn on top of each other. The center of a star is a pentagon with internal angle measure 108. The isosceles triangles on the ends of each star have base angles 72 degrees, and the top angle 36 degrees.

consider this figure as two seperate stars . then consider anyone star , it consist of a regular pentagon at centre & each angle of pentagon is 108 degree then base angles will be 72 degree & the vertex angle be 36 degree & this is the ans.

the 10 pointed star is actually just two 5 pointed star.. in a five pointed star the inner part is a equiangular pentagon which has a total angle of 540 or an angle of 108 per intersection.. a line has 180 degrees minus 108 which is equal to 72, both base of the triangle has an ange of 72 making it 144 .. a triangle has a total of 360 degrees so 360-144=36

360/10=36 answer