Difference between Plane Angle and Solid Angle:
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A solid angle is a 3D angular volume that is defined analogously to the definition of a plane angle in two dimensions. A plane angle, θ, made up of the lines from two points meeting at a vertex, is defined by the arc length of a circle subtended by the lines and by the radius of that circle, as shown below.
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A plane angle is a measurement around a point in 2D object, whereas solid angles are for 3D objects. The angle of a triangle is a plane angle, whereas the angle made by the corner of a room is solid.
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