Question

Which statement are true about the angles in the diagram? Check all that apply

Answer 1

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