Is this a regular polygon?

The sum of the internal angles of a regular polygon is given by this formula:

S = (n - 2) × 180° where n is the number of sides.

But also, the sum of the external angles is always 360°

The external angle at each corner = 180° minus internal angle

In this case, each external angle would need to be 180-153 = 27°

How many 27's are there is 360? Answer 13.333
Not a whole number.

Therefore, this can not be a regular polygon.

Let n be the number of sides with an interior angle 153°.

Sum of interior angles :
(n - 2) × 180° = 153n°
180n - 360 = 153n
27n = 360
n = 360/27
n = 40/3

As n is not an integer, there is no regular polygon with an interior angle of 153°.

Hence, it is NOT a regular polygon.

The external angle is 180-153=27.
If the polygon is regular, all external angles are equal and (it being a convex polygon) they add up to 360.
If this polygon is regular, there will be 360/27=40/3 sides.
This is not a whole number, so the polygon cannot be regular.

Is 153° of the form (n - 2) / n * 180° ?
If so, then 1 - 2/n = 153/180 = 51/60 = 17/20
So 2/n would be = 1 - 17/20 = 3/20
So n = 40/3, which is not a whole number.
So no.