Q. 425.0( 2 Votes )

# In the given figure, ∠AOB = 90° and ∠ABC = 30°. Then, ∠CAO = ?

A. 30^{o}

B. 45^{o}

C. 60^{o}

D. 90^{o}

Answer :

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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