Interior Angles of Shapes

Shapes play a vital part in geometry. Each shapes possess different properties. When two rays intersect at its endpoint, and the plane figure formed at the point at which it intersects is called as Angles. Basically, any shape possesses two types of angles. They are the exterior angles and the interior angles. In this article, we shall discuss about the interior angles of shapes. Also we shall see some shapes with their interior angles.

 

Formula to determine the Interior angles of Shapes:

 

 Normally, the interior angle of any polygon can be determined by using the formula,

         `(180(n)-360)/n`

where n is the number of sides for the shapes.

Now let us determine the interior angles for some shapes.

 

Example Problems Regarding Interior angles of Shapes:

 

Example 1:

 Determine the interior angle of a rectangle.

Solution:

   The formula to determine the interior angle is

              `(180(n)-360)/n`

           where n is the number of sides.

   The rectangle has 4 sides.

     The interior angle of rectangle can be determined by substituting n=4 in the formula,

   Interior angles of a Rectangle = `(180(4)-360)/4`

                                                          =  `(720 - 360)/4`

                                                          = `360/4`

                                                          = 90°

interior angle of a rectangle

Therefore the interior angles of a rectangle measures 90° each.

 

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Example 2:

 Determine the interior angle of a octagon.

Solution:

   The formula to determine the interior angle is

              `(180(n)-360)/n`

      where n is the number of sides.

   The octagon has 8 sides.

   The interior angle of octagon can be determined by substituting n=8 in the formula,

   Interior angles of an Octagon = `(180(8)-360)/8`

                                                         =  `(1440 - 360)/8`

                                                         = `1080/8`

                                                         = 135°

octagon_measure of interior angle

Therefore the interior angles of an octagon measures 135° each.

Example 3:

 Determine the interior angle of a decagon.

Solution:

   The formula to determine the interior angle is

              `(180(n)-360)/n`

       where n is the number of sides.

   The decagon has 10 sides.

   The interior angle of decagon can be determined by substituting n=10 in the formula,

   Interior angles of a Decagon = `(180(10)-360)/10`

                                                        =  `(1800 - 360)/10`

                                                        = `1440/10`

                                                        = 144°

Interior angle of a decagon

Therefore the interior angles of a decagon measures 144° each.

 

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