Question

Geometry math question no Guessing and Please show work

Answer 1

We will follow this strategy: we will find the value of x using a theorem about the sum of interior angles of any polygon, and then we will compute 2x to find A.

The theorem states that the sum of the interior angles of any polygon with $n$ sides is $(n-2)\times 180^\circ$

Your polygon has seven sides (so $n=7$), and the sum of the interior angles is

$10x + 2(2x) + 4(4x) = 10x + 4x + 16x = 30x$

So, using the theorem, we know that

$30x = (7-2)\times 180= 5\times 180 \iff x = \cfrac{5\times 180}{30} = 5 \times 6 = 30$.

Since $x = 30$ and $A = 2x$, we have $A = 2\cdot 30 = 60$