Question

Geometry math question please help

Answer 1

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

$(n-2)\times 180$

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

$2x+4x+4x+4x+4x+2x+10x = (7-2)\times 180$

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:

$30x = 5\times 180 = 900$

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

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

Finally, the required angles is $2x = 2\times 30 = 60$