Question

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

Answer 1

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°