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Answer:
∠BCD = 55°
Step-by-step explanation:
The given triangle ABC is an isosceles triangle, since two sides AB and AC are equal to each other.
By using the property of isosceles triangle, we can conclude that ∠ABC = ∠ACB.
Using angle sum property in ∆ ABC
⇒ ∠ABC + ∠ACB + ∠BAC = 180°
⇒ ∠ACB + ∠ACB + 42° = 180°
⇒ 2∠ACB = 180° - 42°
⇒ ∠ACB = 138°/2
⇒ ∠ACB = 69°
Now, we can see that ∠ACB consists of ∠ACD and ∠BCD.
⇒ ∠ACB = 69°
⇒ ∠ACD + ∠BCD = 69°
⇒ 14° + ∠BCD = 69°
⇒ ∠BCD = 69° - 14°
⇒ ∠BCD = 55°
Hence the required angle is of 55°.
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