Respuesta :

SaniShahbaz

Answer:

  • The sum of the interior angles of the 15-gon [tex]=\:2340^0[/tex]
  • Each interior angle of the regular polygon [tex]=\:156^0[/tex]

Step-by-step explanation:

As we know that

In any convex polygon, if we may start at one vertex and draw the diagonals to all the other vertices, we would form triangles,

The number of triangles thus formed would always  2  LESS than the number of sides.

As

  • The sum of measure of the angles of any triangle is 180°.

Thus,

The sum of the interior angles of the 15-gon will be:

[tex]13\:\times\:180\:=\:2340^0[/tex]

Also

15-gon is regular, it means this total [tex]2340^0[/tex] is shared in equal proportion among the 15 interior angles.

And

Each interior angle of the regular polygon will be:  [tex]\frac{2340^{0} }{15}=156^{0}[/tex]

Therefore, we conclude that:

  • The sum of the interior angles of the 15-gon [tex]=\:2340^0[/tex]
  • Each interior angle of the regular polygon [tex]=\:156^0[/tex]

Keywords: regular polygon, 15-gon, triangle

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