Question

Geometry math question please help

Answer 1

You need this key result: in any polygon, the sum of the interior angles is

`(n-2)* 180`

where
`n` 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

`2x+4x+4x+4x+4x+2x+10x = (7-2)* 180`

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:

`30x = 5* 180 = 900`

and we can solve this equation for
`x` by dividing both sides by 30:

`x = \cfrac{900}{30} = 30`

Finally, the required angles is
`2x = 2* 30 = 60`