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The sum of the exterior angles of a polygon sum to 360o

For a regular polygon, they are all the same size

⇒ dividing 360o by the exterior angle gives the number of sides.

Interior angle = 154o ⇒ exterior angle = 180o - 154o = 26o

⇒ number of sides = 360o ÷ 26o = 1311/13 sides

But a polygon must have a whole number of sides

⇒ 154o cannot be the interior angle of a regular polygon.

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