In the diagram, the tangent MN makes an angle of 55o with the chord PS. IF O is the centre of the circle, find < RPS

In the diagram, the tangent MN makes an angle of 55o with the chord PS. IF O is the centre of the circle, find < RPS

Answer Details

Join SR
< PRS = 90${}^{?}$(Angle in a semicircle)
< PRS = 55${}^{?}$ (Angle between a chord and a tangent = Angle in the alternate segment)
< PSR + < PRS + < RSP = 180${}^{?}$
90v + 55${}^{?}$ + < RSP = 180${}^{?}$
< RSP = 180${}^{?}$ - 145${}^{?}$
= 35${}^{?}$