If point I is the heart of ⊿ABC, then: ∠ CAI = (1/2) ∠ CAB = 25, ∠ ACI = (1/2) ∠ ACB = 30.

∴∠aic= 180-(∠ Cai+∠ ACI) =180-(25+30) =125;

∠∠ADE =∠ABC = 70； DE=AD。

∴∠dea=∠dae=( 180-∠ade)/2 =( 180-70)/2 = 55。

Then ∠ DEA+∠ AIC = 180 So points A, I, C and E are all on the same circle.

∴∠DEI=∠CAI=25。