In Fig. 16.196, if ∠ AOB = 80° and ∠ ABC =30°, then find ∠ CAO .

Question

In Fig. 16.196, if &#x2220; AOB = 80&#xB0; and &#x2220; ABC =30&#xB0;, then find &#x2220; CAO .

Philoid · Accepted Answer

2 ∠OAB = 100°

∠OAB = 50°

Therefore,

∠OAB = ∠OBA = 50°

∠AOB = 2 ∠BCA (Angle subtended by any point on circle)

80° = 2 ∠BCA

∠BCA = 40°

Now,

In triangle ABC

∠A + ∠B + ∠C = 180°

∠A + 30^o + 40^o = 180°

∠A = 110°

∠CAB = ∠CAO + ∠OAB

110° = ∠CAO + 50°

∠CAO = 60°