Question
In a triangle ABC, BC is produced to D so that CD = AC. If ∠BAD = 111° and ∠ACB = 80°, then the measure of ∠ABC is:
Answer: Option D
According to question,
Given :
AC = CD
∠BAD = 111°
∠ACB = 80°
∴ ∠ACD = 180° - 80°
∠ACD = 100°
In isosceles triangle ACD
  ∠ACD + ∠CAD + ∠ADC = 180°
  2∠CAD = 180° - 100°
  ∠CAD = 40°
∴ ∠CAB = 111° - 40° = 71°
∴ ∠ABC = 180° - 71° - 80°
  ∠ABC = 29°
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According to question,
Given :
AC = CD
∠BAD = 111°
∠ACB = 80°
∴ ∠ACD = 180° - 80°
∠ACD = 100°
In isosceles triangle ACD
  ∠ACD + ∠CAD + ∠ADC = 180°
  2∠CAD = 180° - 100°
  ∠CAD = 40°
∴ ∠CAB = 111° - 40° = 71°
∴ ∠ABC = 180° - 71° - 80°
  ∠ABC = 29°
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