Question

Find the value of x in the following figure.

Answer 1

The sum of all exterior angles on a polygon  = 360 degrees.

Therefore you can make this formula:

360 = 46 + (12x + 37) + (12x - 2 ) + (20x - 29)

Now let's solve for x.

360 = 46 + (12x + 37) + (12x - 2 ) + (20x - 29)
360 = 46 + 12x + 37 + 12x - 2 + 20x - 29
360 = 83 + 12x + 12x - 2 + 20x - 29
360 = 81 + 12x + 12x + 20x - 29
360 = 52 + 12x + 12x + 20x
360 = 52 + 24x + 20x
360 = 52 + 44x
308 = 44x
/44      /44
   7 = x

Therefore, x is equal to 7. You can substitute this into each angle to find the actual measurement of each angle. You will notice that the finished angles will all add up to 360 degrees.

Hope it helped :P