Question

In the figure below, O is the centre of the circle and ∟EAD=40º,∟BCD=118º

Find giving reasons

1. ∟ADE 
2. reflex ∟EOD
3. ∟EBD 
4. ∟EAB
5. ∟DAB

Answer 1

1. ∟ADE = 50°
   (∟AED =90°− Ls in a semi-circle)
2. reflex ∟EOD =360 − (40×2)
                      =360 −80 =280°
   (∟ at centre =2∟ on circumference)
3. ∟EBD=40°
   (∟s in same segment)
   (or ∟s subtended by the same chord/arc)
4. ∟EAB=90°
   (∟s in a semi-circle)
5. ∟DAB =180 − 118 = 62°
   (Opp. ∟s in a cyclic quad are supp.).