Definition:Spherical Angle

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Let $S$ be a sphere.

Let $PQ$ be a diameter of $S$.

Let $PAQ$ and $PBQ$ be great circles on $S$ both passing through the points $P$ and $Q$.

Let tangents $S$ and $T$ to $PAQ$ and $PBQ$ respectively be drawn through $P$.


Then the angle between $S$ and $T$ is known as the spherical angle between $PAQ$ and $PBQ$.

Thus a spherical angle is defined with respect only to $2$ great circles.