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Solution


Q.

In Fig, if ∠AOC = 110° then which of the below statements are correct

(i) Value of ∠D is 55°
(ii) Value of ∠D is 110°
(iii) Value of ∠B is 25°
(iv) Value of ∠B is 125°

Choose the correct option from the following:
 
1 (i) and (ii)  
2 (iii) and (iv)   
3 (i) and (iv)   
4 (i) and (iii)  

Ans.

(3)

We know that the angle subtended by a chord at the centre is twice the angle subtended by it on the circumference.

∠AOC=2∠ADC110°=2∠ADC⇒∠ADC=55°⇒∠D=55°

∴ ∠AOC = 110°⇒ Reflex ∠AOC = 360° – 110° = 250° (As shown in Fig.)

Also, reflex ∠AOC = 2∠ABC250°=2∠ABC⇒∠ABC=125°

⇒ ∠B = 125° ⇒ Statements (i) and (iv) are correct.