9.1) OC and OD are radii forming isosceles triangle COD and (Ô1) BOC=110° is the external angle so the two equal angles (Ĉ3 and D̂2) are 110/2=55°=D̂2.
9.2) ∠A=½∠COD (Ô2)=½(180-110)=35° (angle at the centre is twice the angle at the circumference in the same segment; and angles BOC (Ô1) and COD (Ô2) are supplementary).
9.3) ∠B=∠A=35° (angles in the same segment, standing on chord CD).
9.4) ∠ACD=∠ACO (Ĉ2)+∠OCD (Ĉ3)=10+55=65°; ∠A=35°, so ∠ADC=180-(65+35)=80° (angles in triangle ACD).
9.5) ∠N=90° (angle in a semicircle is a right angle). ∠ADC=80° (see 9.4). ∠ADB (D̂1)+∠BDC (D̂2)=∠ADC, ∠ADB (D̂1)+55=80, making ∠ADB (D̂1)=80-55=25°=∠NDQ (D̂5) (alternate angles at an intersection). ∠Q=90-25=65° (right triangle DNQ).