Is there a regular polygon with angles of 158 degree?

Answer 1

Nope, sorry honey. A regular polygon has all interior angles equal, so if one angle is 158 degrees, all angles would have to be 158 degrees. But the sum of interior angles in a polygon is (n-2)*180 degrees, where n is the number of sides. So for a regular polygon with angles of 158 degrees, you'd need n=11 sides, which doesn't work because a regular polygon must have at least 3 sides.

Answer 2

No.

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