angle acd is supplementary to angles ace and bcd and congruent to angle bce. which statements are true about…

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.

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.

Answer

Answer:

  1. Angle BCE is supplementary to angle ACE.
  2. Angle BCD is supplementary to angle BCE.
  3. Angle BCD is congruent to angle ACE.

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is 180°. Since ∠ACD + ∠ACE=180° and ∠ACD + ∠BCD = 180°, and ∠ACD=∠BCE, we know that ∠BCE+∠ACE = 180° and ∠BCD+∠BCE = 180°.

Step2: Recall congruent - angle definition

Two angles are congruent if they have the same measure. Given that ∠ACD is congruent to ∠BCE and ∠ACD+∠ACE = 180°, ∠BCE + ∠BCD=180°, we can conclude that ∠BCD is congruent to ∠ACE.