Question

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Answer 1

x=37

Explanation:

If you stare at the picture long enough you can tell that you have six straight angles, which add up to
`180\°* 6 = 1080\°`. You now need to take away the internal angles, that add up to
`180\° * 6-360\° = 720\°`*

What you have left is two expression of the same quantity - the sum of the external angles. In one case is
`360\°` (the difference between the two values) and in the other is the sum of the various expressions containing x.
`2x +(x+10)+(x+18)+3x+(x-1)+x = 360\\9x = 360 - 27 \rightarrow 9x = 333\rightarrow x=37`

*Pick any point inside the polygon, and join it to the corners. You will create as many triangles as you have sides - in our case 6. Sum of angles will be 180 times the number of sides, minus a whole round angle - the one in the center.