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Question
Given: ∠CAB = 75° and ∠CBA = 50°. Find the value of ∠DAB + ∠ABD.
Sum
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Solution
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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