# If the exterior angles of a convex octagon are x+11,3x-2,2x+6,3x+15,3x-17,4x-6,4x-9 and 5x, calculate the largest of the eight angles?

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### Sohini Khan

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The sum of the exterior angles of any convex polygon is 360°, so if we add up the given exterior angles, we can find x: x+11 + 3x-2 + 2x+6 + 3x+15 + 3x-17 + 4x-6 + 4x-9 + 5x = 360 25x - 2 = 360 25x = 362 x = 362/25 = 14.48 The short method of identifying the largest exterior angle is by comparison/eye: The first is less than 2x, the second is around 3x, the third is less than 3x, the fourth is around 4x, the fifth is less than 2x, and the sixth and seventh are less than 4x, all of which are less than 5x, so 5x must be the largest exterior angle. Calculated, this is 72.4°. If you’re unsure about comparing them by eye, the long way is just substituting x into each angle. This value of x makes our exterior angles: 25.48, 41.44, 34.96, 58.44, 26.44, 51.92, 48.92, and 72.4.

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