why angles of a hexagon are 122 degree 95 degree 80 degree 135 degree and 125 degree find the sixth angle

2 thoughts on “why angles of a hexagon are 122 degree 95 degree 80 degree 135 degree and 125 degree find the sixth angle”

1. Given:

   • We are given five hexagon angle, that is, 122°, 95°, 80°, 135° and 125°.

   Need to find:

   • We need to find the sixth angle of hexagon.

   Solution:

   « Let us consider that, the sixth angle of hexagon be ‘x‘.

   We know that, if we are given with the five angles of a hexagon, we have the required statement, that is,

   • The sum of all six angles of a hexagon is 720°.

   « Plugging all the given angles in the statement, we get:

   → 122 + 95 + 80 + 135 + 125 + x = 720

   → 217 + 80 + 135 + 125 + x = 720

   → 297 + 135 + 125 + x = 720

   → 432 + 125 + x = 720

   → 557 + x = 720

   → x = 720 – 557

   → x = 163.

   ∴ The sixth angle of a hexagon is 163°.

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2. Given:-

   A hexagon with angle 122,95,80,135,125

   To Find :-

   Sixth angle

   Solution :-

   Hexagon It is a six sided polygon. It is a closed polygon. The sum of all angles in a hexagon is 720. Hexa means six and gon means side

   [tex] \sf 122 + 95 + 80 + 135 + 125 + y =720 [/tex]

   [tex] \sf 217 + 215 + 125 + y = 720 [/tex]

   [tex] \sf432 + 125 + y = 720 [/tex]

   [tex] \sf 557 + y =720[/tex]

   [tex]\sf y = 720 – 557[/tex]

   [tex]\star \sf y = 163^{ \circ}[/tex]

   Verification

   122 + 95 + 80 + 135 + 125 + y =720

   122 + 95 + 80 + 135 + 125 + 163 = 720

   217 + 215 + 288 = 720

   432 + 288 = 720

   720 = 720

   Hence verified

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