Question

[2016]
3. In the figure given, O is the centre of the
circle. ZDAE = 70°. Find giving suitable
reasons, the measure of
(i) ZBCD
(ii) ZBOD
(iii) ZOBD
С
O
D
B
A
E​

Answer 1

Answer:

20 degree.

Step-by-step explanation:

Given that:

∠DAE=70  

∘

 

(i)∠BCD

∠BAD=180  

∘

−∠DAE    (By Linear Pair)

=180  

∘

−70  

∘

=110  

∘

 

∠BCD+∠BAD=180  

∘

   (By opposite angles properties of a cyclic quardilateral)

⇒∠BCD=180  

∘

−110  

∘

=70  

∘

 

(ii)∠BOD=2∠BCD=2×70  

∘

=140  

∘

    (Angle subtended by an arc at the centre is double of the angle subtended at the circumference.)

(iii)∠OBD=  

2

1

​  

(180  

∘

−∠BOD)   (By properties of  triangle )

=  

2

1

​  

(180  

∘

−140  

∘

)

=20  

∘