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If the interior angles are 158o, then the exterior angles are 180o - 158o = 22o

For all polygons, the sum of the exterior angles is 360o.

For a regular polygon, they are all the same, so:

exterior_angle x number_of sides = 360o

⇒ number_of_sides = 360o ÷ exterior_angle

= 360o ÷ 22o

= 164/11

A polygon must have a whole number of sides, thus there is no regular polygon with all interior angles 158o

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