Question
Given: ∠CAB = 75° and ∠CBA = 50°. Find the value of ∠DAB + ∠ABD.
✓
Answer
In ΔABC, ∠CBA = 50° ,∠CAB = 75°
∠ACB = 180° - (∠CBA + CAB)
= 180° - (50° + 75° )
= 180° - 125°
= 55°
But ∠ADB = ∠ACB = 55°
(Angle subtended by the same chord on the circle are equal)
Now consider ΔABD,
∠DAB + ∠ABD + ∠ADB = 180°
⇒ ∠DAB +∠ABD + 55° = 180°
⇒ ∠DAB +∠ABD = 180° - 55°
⇒ ∠DAB + ∠ABD = 125°
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