Q42 of 141 Page 447

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°

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