In the given figure, ∠AOB = 90° and ∠ABC = 30°. Then, ∠CAO = ?
Given: and
Construction: join CD
We know that,
∠AOB = 2 × ∠ACB
90° = 2 × ∠ACB
∠ACB = = 45°
Similarly,
∠COA = 2 × ∠CBA
∠COA = 2 × 30
∠COA = 60°
Here,
∠COD + ∠COA = ∠AOD
∠COD + 60° = 180°
∠COD = 180° – 60° = 120°
Again
∠COD = 2 × ∠CAO
∠CAO = = 60°
∴∠CAO = 60°