Geometry Hexagon

Geometry Hexagon

Hexagon is the two dimensional geometric closed figure with five sides.

Geometry Hexagon interior angle:

The angle that found inside the geometric figure is said to be interior angle of the Hexagon.

Geometry Hexagon Exterior angle:

The angle between any side of the Hexagon and the line extended from the next side is said to be exterior angle of the Hexagon.

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Formula:

Formula for calculating the exterior angle of the Hexagon:

Sum of the exterior angle of the Hexagon is 360 degrees.

Formula for calculating the interior angle of the Hexagon:

Sum of Interior angle of the Hexagon = (n-2) 180 degrees

Here n is the number of the Hexagon.

Regular Hexagons:

The regular Hexagon is the geometric figure  in which all sides are equal in length and all the angles are equal in degrees.

Interior angle of the regular Hexagon is `(((n-2) 180)/n)`

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Model Problems:

1.Find the sum of interior angle and each interior angle of the regular geometry Hexagon?

Solution:

To find the sum of the interior angle:

Here

Sum of the interior angle of Hexagon = (n-2) 180 degrees

Here n = 6 sides

= (6-2) 180

= (4) 180

Sum of the interior angle of Hexagon =720 degrees.

To find the each interior angle:

Here

Interior angle of the regular Hexagon =` (((n-2) 180)/n)`

= (((6-2)180)/5)

= (720/6)

Interior angle of the regular Hexagon = 120 degrees.

2. Find sixth interior angle of the Geometry Hexagon when first five angles are 108, 110, 106, 102, 104 degrees respectively?

Solution:

We know that sum of the interior angle of the Hexagon = 720 degrees

That is (angle 1+angle2+angle 3+angle 4+angle 5 +angle 6) = 720

(108+110+106+102+104+x) = 720

(530+x) = 720

x = 720-530

Sixth interior angle of the Hexagon x = 190 degrees

3. Find first interior angle of the Geometry Hexagon when last five angles are 108, 110, 108, 106, 104 degrees respectively?

Solution:

We know that sum of the interior angle of the Hexagon = 720 degrees

That is (angle 1+angle2+angle 3+angle 4+angle 5 +angle 6) = 720

(x+108+110+108+106+104) = 720

(x+536) = 720

x = 720-536

Sixth interior angle of the Hexagon x = 184 degrees