Question

In the following figure; AC = CD, AD = BD and ∠C = 58°.

Find the angle CAB.

Answer 1

In ΔACD,

AC = CD                     ...[Given]

∴ ∠CAD = ∠CDA

∠ACD = 58°                ...[Given]

∠ACD + ∠CDA + ∠CAD = 180°

⇒ 58° + 2∠CAD = 180°

⇒ 2∠CAD = 122°

⇒ ∠CAD = ∠CDA = 61°      ...(i) 

Now,

∠CDA = ∠DAB + ∠DBA              ...[Ext. angle is equal to sum of opp. int. angles]

But,

∠DAB = ∠DBA                ...[Given: AD = DB]

∴ ∠DAB + ∠ DAB = ∠CDA

⇒ 2∠DAB = 61°

⇒ ∠DAB = 30.5°             ...(ii)

In ΔABC,

∠CAB = ∠CAD + ∠DAB

∠CAB = 61° + 30.5°

⇒ ∠CAB = 91.5°