What is the sum of the angles in a pentagon?

The sum of the interior angles of a polygon can be determined using the formula ( (n - 2) \times 180 ) degrees, where ( n ) is the number of sides in the polygon. For a pentagon, which has five sides, you would substitute ( n = 5 ) into the formula:

[ (5 - 2) \times 180 = 3 \times 180 = 540 \text{ degrees} ]

This means that the total measure of all the interior angles in a pentagon is indeed 540 degrees. This calculation aligns with the properties of polygons and is foundational in geometry, making the answer consistent and reliable.