Given definition is not a math. An angle is the union of two non collinear rays with a common endpoint is called vertex of the angle and the rays are called the sides.
What is collinear and non collinear rays ?
Non collinear point are three or more points that are not contained on the same time. collinear point lie on the same line. A From this we can define angles. non collinear rays that share the same endpoint form an angle.
You can see by figure
Learn more about the collinear and non collinear lines here:
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