In order for a 25-gon to be regular

d. All interior angles and all sides are parallel.

Explanation:

The question is incomplete.

The complete question is:

In order for a 25-gon to be regular, which of the following statements must be true?

a. The interior angles are congruent to their exterior angles.

b. All the diagonals are congruent.

c. Opposite pairs of sides are parallel.

d. All interior angles and all sides are congruent

Solution to the problem

A 25-gon is a polygon with 25 sides.

By definiton all sides and all angles of a regular polygon are equal. Hence, you can assert promptly that the correct anwer is the last choice: d. All interior angles and all sides are congruent.

As for the other choices you can analyze each one in this way.

a. The interior angles are congruent to their exterior angles.

The exterior angles are the angles formed by the extension of a side and the next side.

The exterior angles of a polygon sum 360°, then if the polygon is regular the measure of each exterior angle 360° divided by the number of sides.

For the regular 25-gon, that is: 360º/25 = 14.4º.

On the other hand, an exterior angle and the interior angle next to are supplementary. Thus, the measure of the interior angle will be 180º - 14.4º = 165.6º. Clearly, they are not congruent.

b. All the diagonals are congruent.

The diagonals are the sements that joint two non-consectuive sides. There are many differnt diagonals, and most of them have different lengths. Hence, this is false.

c. Opposite pairs of sides are parallel

Only poygons with an even number of sides have opposite side paralles. For instance, square and hexagon. Imagin a triangle or a pentagon: they cannot have parallel opposite sides.

Hence, this is false too.

The only true stament is the last one, as stated and explained above.