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

In ∆ABC, by angle sum property we have

⇒ ∠ACB + ∠CBA + ∠CAB = 180°

⇒ ∠ACB + 50° + 75° = 180°

⇒ ∠ACB + 125° = 180°

⇒ ∠ACB = 180° - 125° = 55°.

We know that,

Angles subtended by the same chord on the circle are equal.

⇒ ∠ADB = ∠ACB = 55°.

Now, taking ∆ABD

⇒ ∠DAB + ∠ABD + ∠ADB = 180° [Angle sum property]

⇒ ∠DAB + ∠ABD + 55° = 180°

⇒ ∠DAB + ∠ABD = 180° - 55°

⇒ ∠DAB + ∠ABD = 125°

Hence, ∠DAB + ∠ABD = 125°.