The answer is no.
It is true of triangles, but not necessarily of other polygons.
A good counterexample is the Rhombus.
You can define a Rhombus as a quadrilateral with 4 congruent ( equal) sides.
However, only the opposite angles are equiangular, not all 4 angles.
Picture, if you will, a very elongated Rhombus to easily see this.
The only equiangular Rhombus is the Square.
Many regular polygons are equiangular but not all.
A regular polygon has equal angles AND sides.
Not only can a regular polygon have equal angles and sides, it must have them.
A polygon with sides of equal length and equal angles is termed a regular polygon.
A polygon with four equal angles and sides is a square.
A polygon has 3 or more sides and is called regular when all sides and angles are equal and it is irregular when its sides and angles are not equal.
A regular polygon has equal angles AND sides.
Not only can a regular polygon have equal angles and sides, it must have them.
A polygon with sides of equal length and equal angles is termed a regular polygon.
A polygon with four equal angles and sides is a square.
A regular polygon has equal sides in length and angles.
A regular polygon
A Regular Polygon.
A REGULAR Polygon.
A polygon with 6 equal sides and angles is called a hexagon.
A polygon has 3 or more sides and is called regular when all sides and angles are equal and it is irregular when its sides and angles are not equal.
Polygons have an equal number of sides and angles.
A polygon whose sides are not equal is known as an irregular polygon. A regular polygon has equal sides and angles.