Question

angle acd is supplementary to angles ace and bcd and congruent to angle bce. which statements are true about the angles in the diagram? select three options. angle ace is supplementary to angle bcd, angle bce is supplementary to angle ace, angle bcd is supplementary to angle bce, angle ace is congruent to angle bce, angle bcd is congruent to angle ace.

Explanation:

1. Given ∠ACD is supplementary to ∠ACE and ∠BCD, so ∠ACD + ∠ACE = 180° and ∠ACD + ∠BCD = 180°. By transitive property, ∠ACE = ∠BCD (so ∠BCD is congruent to ∠ACE, last option is true).
2. ∠ACD ≅ ∠BCE (given). Since ∠ACD + ∠ACE = 180°, then ∠BCE + ∠ACE = 180° (so ∠BCE is supplementary to ∠ACE, second option is true).
3. ∠ACD + ∠BCD = 180°, and ∠ACD ≅ ∠BCE, so ∠BCE + ∠BCD = 180° (so ∠BCD is supplementary to ∠BCE, third option is true).
4. ∠ACE and ∠BCD are congruent, not supplementary (first option false).
5. ∠ACE and ∠BCE: ∠ACE + ∠BCE = 180° (supplementary), not congruent (fourth option false).

Answer:

B. Angle BCE is supplementary to angle ACE
C. Angle BCD is supplementary to angle BCE
E. Angle BCD is congruent to angle ACE