You need this key result: in any polygon, the sum of the interior angles is
[tex] (n-2)\times 180 [/tex]
where [tex] n [/tex] is the number of sides of the polygon.
Your polygon has seven sides, and the measures of all angles are given. So, we can write
[tex] 2x+4x+4x+4x+4x+2x+10x = (7-2)\times 180 [/tex]
Again, we've simply written that the sum of all interior angles is the number of sides, minus two, times 180.
We can simplify both sides: we sum like terms on the left hand side, and we easily compute the right hand side:
[tex] 30x = 5\times 180 = 900 [/tex]
and we can solve this equation for [tex] x [/tex] by dividing both sides by 30:
[tex] x = \cfrac{900}{30} = 30 [/tex]
Finally, the required angles is [tex] 2x = 2\times 30 = 60 [/tex]
