In the figure given below O is the center of the circle and CD=DE=EF=FG if ∠COD=40 then the value of reflex ∠COG

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200∘

220∘

250

280∘

answer is A.

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Detailed Solution

The correct answer is: 200∘
Using standard condition of chords:

P Q = R S

then

∠ P O Q = ∠ S O R

Using the given figure:

⇒ ∠ C O D = ∠ D O E = ∠ E O F = ∠ F O G

Angle

∠ C O G

is divided into four parts

∠ C O G = ∠ C O D + ∠ D O E + ∠ E O F + ∠ F O G ⇒ ∠ C O G = ∠ C O D + ∠ C O D + ∠ C O D + ∠ C O D ⇒ ∠ C O G = 4 ∠ C O D

Now,

∠ C O D = 40 °

∠ C O G = 4 × (40 °) ⇒ ∠ C O G = 160 °

The condition that reflex of

θ

360 ∘ − θ

⇒ r e f (∠ C O G) = 360 ° − ∠ C O G ⇒ r e f (∠ C O G) = 360 ° − 160 ° ⇒ r e f (∠ C O G) = 200 °

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