The chords EH and FG of the circle are produced to meet at X. Given that $$\angle EGH\ =\ 40\degree$$  and XH = HF = FE, calculate $$\angle HXG$$  

(a)  

In the circle, the diameter QS intersects the chord PR at M, the midpoint of PR. Given that O is the centre of the circle and $$\angle POQ\ =\ 136\degree$$  , calculate $$\angle RSQ$$  

(a)  

SET is a tangent to the circle, centre O. Given that DE = DF and $$\angle FET\ =\ 36\degree$$  , calculate $$\angle DES$$  

(a)  

ABCD is a cyclic quadrilateral with AD = AB and AD is produced to E. If $$\angle CDE\ =\ 70\degree$$  and $$\angle CDB\ =\ 72\degree$$  , calculate $$\angle BAD$$  

(a)  

EFGH is a cyclic quadrilateral with EH parallel to FG. DG is a diameter of the circle, centre O. Given that $$\angle DOH\ =\ 82\degree$$  and $$\angle DGE\ =\ 17\degree$$  , calculate $$\angle HEG$$  

(a)  

A, B, C, D and E are points on a circle. AB = AE, $$\angle EAB\ =\ 130\degree$$  and $$\angle EDC\ =\ 110\degree$$  , calculate $$\angle ABC$$  

(a)  

TKXM and SNXL are two tangents to one of the circles in the diagram. JKL is a straight line. Given that $$\angle TKJ\ =\ 54\degree$$  and $$\angle NJK\ =\ 40\degree$$  , calculate $$\angle LMN$$  

(a)  

(a)  

(a)  

(a)