(a) In triangle CXD, \(\angle CDB=180^\circ-88^\circ-55^\circ=\boxed{37^\circ}\), because triangle angles sum to 180°. \(\angle ABD=\boxed{55^\circ}\), because angles in the same segment subtending chord AD are equal. \(\angle AED=180^\circ-55^\circ=\boxed{125^\circ}\), because opposite angles in cyclic quadrilateral ABDE sum to 180°.

(b)(i) Corresponding sides DX and AX give length ratio \(8/4=2\). Thus \(CX=2(BX)=2(2.7)=\boxed{5.4\text{ cm}}\). (b)(ii) Square the length ratio: \(\boxed{4:1}\).