∠∠ACB = 90°
∴x+y=90
∵AF divides CD vertically, BG divides CE vertically.
∴AC=AD,BC=BE
∴△acd:∠ACD =∠ADC =( 180-∠cab)/2 = 90- 1/2 x
△BCE:∠BCE =∠BEC =( 180-∠CBA)/2 = 90- 1/2y
∠△DCE:∠ECD = 180-∠ADC-∠BEC
∴∠ECD = 180-(90- 1/2 x)-(90- 1/2y)
= 1/2 (x+y)
= 1/2 x90
=45
(2)∠ECD = 90- 1/2a; The reason is:
Let ∠ cab = x, ∠ CBA = y.
∫∠ACB = a
∴x+y= 180 -a
∵AF divides CD vertically, BG divides CE vertically.
∴AC=AD,BC=BE
∴△acd:∠ACD =∠ADC =( 180-∠cab)/2 = 90- 1/2 x
△BCE:∠BCE =∠BEC =( 180-∠CBA)/2 = 90- 1/2y
∠△DCE:∠ECD = 180-∠ADC-∠BEC
∴∠ECD = 180-(90- 1/2 x)-(90- 1/2y)
= 1/2 (x+y)
= 1/2 x( 180 -a)
=90 - 1/2 a
I am glad to solve the above problems for you, and I hope it will help your study! ≤、≥ ∠