It cannot have more than one.
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At each vertex of a triangle, an exterior angle of the triangle may be formed by extending ONE SIDE of the triangle.
The sum of an adjacent interior and its exterior angle will total to 360°. If the angles were to be equal, they would both have to be 180°. An angle of 180° is a straight line. A polygon may be composed of straight lines that intersect at vertices but a straight line has no vertex. That being the case, the answer to your question is "No".
obtuse: greater than 90 degrees right: 90 degrees acute: less than 90 degrees
Any way you like. Some angles are uniquely identified by their vertex. These can be numbered or allocated letters of the alphabet. Both Greek and Roman alphabets are used although with the Roman alphabet, upper case letters are more common. Where the vertex does not identify the angle uniquely, it may be necessary to use the names of three vertices. For example, the angle XYZ is the angle formed by the rays XY and YZ when they meet at Y.
If the vertex angle measures 36 degrees, then each base angle is 72 degrees, regardless of the length of the congruent sides. They may be the length of a DNA strand, a 57 Chevy, or the distance to the Andromeda Galaxy. It doesn't matter. The base angles are still 72 degrees.