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

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°.

  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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