Star Study - 5 pointed individual

Angle of pentagon = 108°

Base angle of isosceles triangle = 180 – 108 = 72°

so internal angle = 180 – (72 + 72) = 36°

$join\quad all\quad points\quad to\quad form\quad a\quad circle\quad \\ Now\quad concider\quad one\quad internal\quad angle\quad the\quad arc\quad which\quad subtend\quad it.\\ In\quad total\quad there\quad are\quad 5\quad of\quad this\quad arc,joined\quad end\quad to\quad end\quad which\quad will\quad subtend\quad a\quad total\quad of\quad 360\quad in\quad centre,\quad so{ \quad 72 }^{ 0 }\quad subtended\quad by\quad one\quad arc\quad in\quad centre,\\ So\quad angle\quad at\quad circumference=72/2=\quad 36\quad degree=\quad internal\quad angle=36\quad degree\\ So\quad 10\quad internal\quad angle=\quad 360\quad degree\quad$

The angle measures of each angle in the center pentagon is 108 degrees. That makes the base angles of the isosceles triangles 72 degrees. So the "tip" angle is 36 degrees.

5a= 180 so, a= 36

Exterior angle of a pentagon= 360/5 =72 , Third angle of a isosceles angled triangle= 180-(72*2) =36

Firstly the figure is a regular star. And there is a regular pentagon forming inside of the star.

As we know that the sum of interior angles of a regular pentagon is equal to 108 deg.

And there are three triangles formed inside this figure and one vertex of every triangles falls in the regular polygon making its vertex too. So again apllying the law of triangles that sum of all interior angles would be equal to 180.

108 + x = 180 x = 72

Now divide the 72 into two equal halves which is to be 36 as the triangles would be isosceles triangle. Now we know that the shaded angle is equal to 36 deg. :)

http://www.mathsisfun.com/geometry/interior-angles-polygons.html

Each angle of a regular pentagon is=(5-2)*180 /5 degree=108 degree.each angle of the triangle outside of the pentagon is=180--108=72 degree.so the internal angle of the pointed vertex is =180--(72+72)=36 degree

if abc is any triangle and angle c to measure, then angle c= 180-a-b, or, c= 180-2a [angle a=angle b] again,summation of pentagon angles= (5-2) 180=540 so, angle of pentagon 540/5=108 =180-a so,a= 72. so,angle c=180-2*72 = 36.

draw a circle circumscribing the star. 360/5 = 72 the arc subtended by the angle whose vertex lies along the circumference. so the angle is 72/2 = 36.