Angle of friction (φ): Angle made by the resultant of normal reaction and limiting frictional force with the normal reaction is called angle of friction.

Angle of repose (θ): The minimum angle of the plane at which the body kept on it starts to slide due to its own weight is called angle of repose

To prove:$ θ=φ \\ ∑Fy=0 \\ N- W \cosθ = 0 \\ N= W \cosθ \\ ∑Fx=0 \\ -W \sinθ + F= 0 \\ F= W\sinθ \\ µN= W \sinθ \\ µW\cosθ= W\sinθ \\ µ = \tanθ \\ but\space \space µ = \tanφ \\ \tanφ = \tanθ \\ φ=θ ---proved$