by vertex or point
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There are three ways to name an angle, provided there are only three points on the angle. Say the vertex is point A, and there are two rays extending. Each has another point on it, points B and C. You can name this angle BAC, CAB, or A.
The 5 ways to prove that two triangles are congruent are to find equal: 1) side-side-side 2) side-angle-side 3) angle-side-angle 4) angle-angle-angle 5) hypotenuse-leg
Well there are many ways to name an angle. You can look up cute angle names on the Internet (Pun intended), or you can take another angle and go to you local bookstore which has many nice name books. You can look in the phone book but not just any, you should look in the right angle phone book for nomenclature ideas. Some people just look around at their friends and see what they named their angles. Or if you are very original you can make up an angle name like apple angle. Seriously, you can name an angle by specifying three points: two on the rays and one at the vertex
obtuse,cute,right,and straight angles
You use the points of the vertex and on the two sides. For example a right angle with a vertex of A and two sides B and C. would be Angle BAC