Two spur gear wheels of \(80 \mathrm{~mm}\) and \(120 \mathrm{~mm}\) pitch diameters have involute teeth of standard addenda of \(3 \mathrm{~mm}\) and \(20^{\circ}\) pressure angle. The module is \(1 \mathrm{~mm}\). Determine

(a) the length of path of contact,

(b) contact ratio, and

(c) angle turned through by pinion, while any pair of teeth is in contact.