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Q: Do all pentagons have congruent angles?

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Yes

Sometimes. For a regular pentagon, all the sides and interior angles are congruent. However, this isn't the case for some pentagons.

No, similar pentagons (or any polygon for that matter) must have corresponding congruent angles and all sides must be proportional to its corresponding sides. For example, if a square with a triangle on it is a pentagon, then a regular pentagon would not be similar to it (because corresponding angles are not congruent).

I assume you mean a regular dodecahedron. A regular dodecahedron has twelve faces, each of which are regular* pentagons. *(all sides are congruent, all angles are congruent)

Two pentagons that have corresponding angles congruent. First equals the first, second equals the second and so forth.

All right angles are congruent, and all straight angles are congruent.

No, not all angles in a trapezoid are congruent. A trapezoid may have two pairs of congruent angles, or may have no congruent angles.

No, pentagons to not have right angles.

Rectangles have all angles congruent,

Some are some are not. Two regular pentagons with one equal side are congruent.

a polygon that has all angles congruent is an equiangular .....

Pentagons do not have to be regular. Elongating one side will skew two angles and make them non congruent with the other three, creating an irregular polygon.

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