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Question -

ABCD is a cyclic quadrilateral in which:
(i) BC || AD, ∠ADC = 110° and ∠BAC = 50°. Find ∠DAC.
(ii) ∠DBC = 80° and ∠BAC = 40°. Find ∠BCD.
(iii) ∠BCD = 100° and ∠ABD = 70° find ∠ADB.



Answer -

(i) It is given that   ,   and  
     
We have to find  
In cyclic quadrilateral ABCD
       ..… (1)
       ..… (2)
Since,   
So,
Therefore in  ,  
So ,                    ..… (3)
Now,                    (  and   is transversal)
 
(ii) It is given that  ,   and  
We have to find  
                     (Angle in the same segment are equal)
 
Hence,  
(iii) It is given that, ∠BCD = 100° and ∠ABD = 70°
As we know that sum of the opposite pair of angles of cyclic quadrilateral is 180°.
Hence,   

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