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Question
In the figure, AB = AC = CD, ∠ADC = 38°. Calculate: (i) ∠ ABC, (ii) ∠ BEC.
Solution
(i) ∵ AC = CD
∴ ∠ CAD = ∠ ADC = 38°
Now, in Δ ACD,
∠ ACD + ∠ CAD + ∠ ADC = 180°
⇒ ∠ ACD + 38° + 38° = 180°
⇒ ∠ ACD = 104°
Now,
⇒ ∠ ACB + ∠ ACD = 180°
⇒ ∠ ACB + 104° = 180°
⇒ ∠ ACB = 76°
Again, AB = AC
∴ ∠ ABC = ∠ ACB = 76°
(ii) In Δ ABC,
∠ BAC + ∠ ABC + ∠ ACB = 180°
⇒ ∠ BAC + 76° + 76° = 180°
⇒ ∠ BAC = 28°
Now, ∠ BEC = ∠ BAC = 28° ....(Angles subtended by the same chord)
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