Final answer:
In △ABE within a regular hexagon, all angles are 60 degrees because it is an equilateral triangle, with each angle being half the interior angle of the hexagon.
Step-by-step explanation:
To find each angle of △ABE in a regular hexagon, we must consider the properties of the regular hexagon and the triangle formed within it. In a regular hexagon, all interior angles are equal, and each measures 120 degrees, since the sum of the angles of a hexagon (4n+2) × 90 degrees, where n is the number of sides beyond 3, gives us (4(6-3)+2) × 90 = (4×3+2) × 90 = (12+2) × 90 = 14 × 90 = 1260 degrees for the entire hexagon and 1260 degrees / 6 sides = 210 degrees per angle. However, considering the symmetry of a regular hexagon, the diagonal BE divides the interior angle at B and E into two equal parts.
Therefore, the angle ABE and the angle AEB are each half of 120 degrees, which is 60 degrees. Since the sum of the angles in △ABE must equal 180 degrees, and we have two angles measuring 60 degrees, the remaining angle at A (BAE) must be 180 degrees - 60 degrees - 60 degrees = 60 degrees.
Hence, all angles in △ABE are alike and are each 60 degrees, meaning △ABE is an equilateral triangle.