The measure of angles of a hexagon are x°,


The measure of angles of a hexagon are x°, (x − 5)°, (x − 5)°, (2x − 5)°, (2x − 5)°, (2x + 20)°. Find the value of x.


Since the sum of all the angles of a hexagon is $720^{\circ}$, we get:

$x^{\circ}+(x-5)^{\circ}+(x-5)^{\circ}+(2 x-5)^{\circ}+(2 x-5)^{\circ}+(2 x+20)^{\circ}=720^{\circ}$

$\Rightarrow x^{\circ}+x^{\circ}-5^{\circ}+x^{\circ}-5^{\circ}+2 x-5^{\circ}+2 x-5^{\circ}+2 x+20^{\circ}=720^{\circ}$

$\Rightarrow 9 x-20^{\circ}+20^{\circ}=720^{\circ}$

$\Rightarrow 9 x=720^{\circ}$

$\therefore x=80$

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