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In the given figure, O is the center of the circle

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In the given figure, O is the center of the circle [#permalink]

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New post 22 Aug 2017, 10:19
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66% (01:24) correct 34% (01:08) wrong based on 38 sessions

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In the given figure, O is the center of the circle; ∠ OAB= 80° and ∠ OCB= 70°, What is the measure of ∠ AOC ?

A) 120°
B) 60°
C) 150°
D) 100°
E) 80°

Kudos if it helps.
[Reveal] Spoiler: OA

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Re: In the given figure, O is the center of the circle [#permalink]

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New post 22 Aug 2017, 10:46
pushkarajnjadhav wrote:
In the given figure, O is the center of the circle; ∠ OAB= 80° and ∠ OCB= 70°, What is the measure of ∠ AOC ?

A) 120°
B) 60°
C) 150°
D) 100°
E) 80°

Kudos if it helps.



Hi..
OAB is 80 and OCB is 70..
So remaining two angles sum : AOC+ABC=360-(80+70)=210..(i)
Also if AOC is extended to the circumference AO'C=AOC/2
And AO'C+ABC=180......AOC/2 + ABC=180....(ii)

From i and ii
AOC/2=30...AOC=30*2=60

B
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Re: In the given figure, O is the center of the circle [#permalink]

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New post 22 Aug 2017, 11:05
∠ OAB + ∠ OCB + ∠ AOC + ∠ ABC =360

80+70+ ∠ AOC + ∠ ABC =360

∠ AOC + ∠ ABC = 210
∠ AOC + 1/2 ∠X = 210 (property of inscribed angle... Here X is the angle measure of larger ARC AOC)

∠ AOC + 1/2 (360 - ∠ AOC) = 210 (property - measure at a point is 360)


Solving we get,
∠ AOC=60

Any other easy way to solve this..?

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Re: In the given figure, O is the center of the circle [#permalink]

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New post 22 Aug 2017, 11:24
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Hi akshata19,
here is an alternate approach.

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Re: In the given figure, O is the center of the circle [#permalink]

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New post 22 Aug 2017, 11:31
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Clearly answer is B
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Re: In the given figure, O is the center of the circle   [#permalink] 22 Aug 2017, 11:31
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