It is given that LXYZ = 64° and XY is produced to point P. Draw a figure from the given infonnation. If ray YQ bisects LZl'P, find LXYQ and reflex LQYP.

Ray YQ bisects LPYZ. • Q z :. LPYZ = LPYQ = LQyz ...(i) Ray yz stands on line PX. < p Y x > .. LPYZ + Lzyx = 180° [Linear pair) 2LPYQ + 64° = 180° [From (i)J 2LPYQ = 180° - 64° = 116° LPYQ = 58° ..•(ii) .. Reflex LQYP = 360° - LPYQ = 360° - 58° = 302°. Also LXYQ = LXYZ + LQyz = 64° + 58° = 122°. [From (i), (ii)]