Question

in the given figure length of arc AB and length of arc BC are in ratio 3:2 if angle AOB = 84° find
1) angle BOC
1) angle CAO
3) angle OBC​

Answer 1

Answer:

Step-by-step explanation:

∡AOB=96  

0

 

AB

:  

BC

=3:2

⇒∡AOB:∡BOC=3:2

⇒  

∡BOC

96  

0

 

​  

=  

2

3

​  

⇒∡BOC=  

3

2

​  

×96  

0

=64  

0

 

Now, Δ  

"

OBC is isosceles   [∵   OB=OC=r]

∴    ∡BOC+2∡OBC=180  

0

 

⇒∡OBC=  

2

180−64

​  

=58  

0

 

also Δ  

"

AOB is isosceles  [because   OA=OB=r]

∴    ∡AOB+2∡OBA=180  

0

 

⇒∡OBA=  

2

180−96

​  

=42  

0

 

∴    ∡ABC=58  

0

+42  

0

=100  

0