Answer:
B. Yes, by the AA Similarity Postulate
Step-by-step explanation:
This triangles are both similar based on the AA Similarity Postulate. We know that all angles are equal because...
m∠ABE = m∠CBD = 42° (because they are veridical/opposite angels)
m∠AEB = 180° - m∠ABE - m∠EAB = 180° - 42° - 53° = 85°
Then from here we know that
m∠BDC = 180° - 85° - m∠CBD
m∠BDC = 95° - 42°
m∠BDC = 53°
From here we see that they are similar because of the AA Similarity Postulate, since
m∠ABE = m∠CBD = 42°
m∠BDC = m∠EAB = 53°
m∠AEB = m∠BCD = 85°
