I is the incentre of a right triangle ABC. If AB = BC, then find the measure of ∠AIC.

In right triangle ABC with AB equal to BC, the angles at vertices A and C are 45 degrees each. The incentre I forms an angle AIC that can be calculated using the formula 90 degrees plus half of angle B. Since angle B is the right angle at 90 degrees, half of angle B is 45 degrees. Adding this to 90 degrees gives an angle AIC measure of 135 degrees.

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