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beks73 [17]
4 years ago
6

Geometry math question no Guessing and Please show work

History
1 answer:
zhuklara [117]4 years ago
8 0

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 <em>any</em> 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

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