Question
In the given figure, AB = AC = CD and ∠ADC = 38°. Calculate:
(i) Angle ABC
(ii) Angle BEC
(i) Angle ABC
(ii) Angle BEC
✓
Answer
(i) AC = CD
∴∠CAD = ∠CDA = 38°
∴∠ACD = 180° - 238° = 104°
∴∠ACB = 180° -104° = 76° (Straight line)
Also, AB = AC
∴ ∠ABC = ACB = 76°
(ii) By angle sum property,
∠BAC = 180° - 2 × 76°
∠BAC = 28°
∴ ∠BEC = ∠BAC = 28° ...(Angles in the same chord)
∴∠CAD = ∠CDA = 38°
∴∠ACD = 180° - 238° = 104°
∴∠ACB = 180° -104° = 76° (Straight line)
Also, AB = AC
∴ ∠ABC = ACB = 76°
(ii) By angle sum property,
∠BAC = 180° - 2 × 76°
∠BAC = 28°
∴ ∠BEC = ∠BAC = 28° ...(Angles in the same chord)
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