(b) x is independent of the triangle
In ΔABC, CA = CB
⇒ ∠CBA = ∠CAB = ∠A
∴ ∠ACB = 180° – 2∠A
∴ ∠ACD = 180° – 2∠A + 90°
= 270° – 2∠A
∵ AC = AB = CD
⇒ AC = CD
⇒ In ΔCAD, ∠CDA = ∠CAD
= \(\frac12\) (180° – (270° – 2∠A)) = ∠A – 45°.
= ∠A – x (∴∠CAE = ∠CAB – ∠EAB = ∠A – x)
⇒ x = 45° So X is independent of the triangle.