what is the definition of an angle?

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An angle is formed by two rays with a common end point. The common end point is called the vertex.

The angle is also measure of deviation from the straight line and is measured by the rotation swept out by a circular arc by a unit radius.

Thus if OX and OP are the two rays with a common vertex O, then with O as centre and with any radius r, draw a circular arc to cut both OA and OP at A and B. Now OA=OB= r.

Then angle x at O formed by the rays OX and OP is given by:

Angle XOP = angle x = Arc AB/radius r.

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