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

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