Answer:
<u><em></em></u>
<u><em>d. All interior angles and all sides are parallel.</em></u>
Explanation:
The question is incomplete.
The complete question is:
<em>In order for a 25-gon to be regular, which of the following statements must be true?</em>
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<em>a. The interior angles are congruent to their exterior angles.</em>
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<em>b.All the diagonals are congruent.</em>
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<em>c.Opposite pairs of sides are parallel.</em>
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<em>d. All interior angles and all sides are congruent</em>
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<h2>Solution to the problem</h2>
<em>A 25-gon is a polygon</em> 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: <em>d. All interior angles and all sides are congruent.</em>
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As for the other choices you can analyze each one in this way.
<u>a. The interior angles are congruent to their exterior angles.</u>
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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.
<u>b. All the diagonals are congruent.</u>
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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.
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<u>c.Opposite pairs of sides are parallel</u>
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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.
