Answer:
Options B,C,E are true.
Explanation:
It has been given in the question ∠ACD is supplementary to ∠ACE and ∠BCD
∠ACD ≅ ∠BCE
Option A. ∠ACE is supplementary to ∠BCD
False. They are not lying on a point of straight line.
∠ACE + ∠BCD ≠180°
Option B. ∠BCE is supplementary to ∠ACE
Since ∠ACD + ∠ACE = 180° [Given]
and ∠ACD ≅ ∠BCE [Given]
Therefore, ∠BCE + ∠ACE = 180°
TRUE.
Option C. ∠BCD is supplementary to ∠BCE
Since ∠ACD + ∠BCD = 180°[Given]
and ∠ACD ≅ ∠BCE [Given]
So ∠BCE + ∠BCD = 180°
TRUE.
Option D. ∠ACE ≅ ∠BCE
Since ∠ACD + ∠ACE = 180°
And ∠ACD + ∠BCD = 180°
This is clear from these equations that ∠ACE is supplementary to ∠BCD.
FALSE :
Option E. ∠BCD is congruent to ∠ACE
As we have already proved in option D. ∠BCD ≅ ∠ACE
TRUE
Therefore, Options B, C, E are TRUE