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

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pushkarajnjadhav
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In the given figure, O is the center of the circle [#permalink] New post   22 Aug 2017, 10:19
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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°

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pushkarajnjadhav
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In the given figure, O is the center of the circle [#permalink] New post   Updated on: 09 Sep 2023, 11:16
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Hi akshata19,
here is an alternate approach.
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Originally posted by pushkarajnjadhav on 22 Aug 2017, 11:24.
Last edited by Bunuel on 09 Sep 2023, 11:16, edited 2 times in total.
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Re: In the given figure, O is the center of the circle [#permalink] New post   22 Aug 2017, 10:46
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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] New post   22 Aug 2017, 11:05
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∠ 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..?

Kudos if the above explanation helped

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Re: In the given figure, O is the center of the circle [#permalink] 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] New post   21 Sep 2019, 08:37
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.


Notice that AOC + 2(ABC) should give you 360 because it is a circle.

AOC+ABC=210 ....sum of angles of a quadrilateral should be 360.
If AOC is 60 then ABC is 150. Double of ABC will be 300. The sum will be 360 which forms the circle. Hence B.

Thank you!
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Re: In the given figure, O is the center of the circle [#permalink] New post   09 Sep 2023, 11:04
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Re: In the given figure, O is the center of the circle [#permalink]
09 Sep 2023, 11:04
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