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Question
The measure of angles of a hexagon are x°, (x − 5)°, (x − 5)°, (2x − 5)°, (2x − 5)°, (2x + 20)°. Find the value of x.
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Solution
\[\text{ Since the sum of all the angles of a hexagon is } 720° , \text{ we get } : \]
\[x° + \left( x - 5 \right)° + \left( x - 5 \right)° + \left( 2x - 5 \right)° + \left( 2x - 5 \right)° + \left( 2x + 20 \right)° = 720°\]
\[ \Rightarrow x° + x° - 5° + x°- 5°+ 2x - 5°+ 2x - 5°+ 2x + 20°= 720° \]
\[ \Rightarrow 9x - 20° + 20° = 720° \]
\[ \Rightarrow 9x = 720° \]
\[ \therefore x = 80\]
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