A quadrilateral is ANY closed figure with 4 sides. Therefore, it also has 4 angles - any of which may, or may not, be congruent. About the only general statement about angles that applies to all quadrilaterals is that the sum of the angles is 360 degrees.
By the way, it is possible for a quadrilateral to have 3 congruent angles, and the fourth angle not be congruent with the other 3.
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No. Very few of them do.
The sum of the interior angles of a quadrilateral is 360 degrees. If three of the angles are right angles, that is, of 90 degrees each, the the fourth must be 90 degrees. So you can have a quadrilateral with three right angles but its fourth angle will also be a right angle. So exactly 3 right angles is not possible.
There can be at most 3 obtuse angles in a quadrilateral.
In an isosceles triangle 2 sides are congruent and 2 angles are congruent. In an equilateral triangle all 3 sides are congruent and all 3 angles are congruent also.
Vertical angles must necessarily be congruent, however congruent angles do not necessarily have to be vertical angles. An example of congruent angles which are not vertical angles are the 3 interior angles of an equilateral triangle. These angles do not share the same vertex yet they are congruent.