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# If arc ABC in the circle above is 80°, then what is the value of x°+y°

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Joined: 02 Sep 2009
Posts: 60681
If arc ABC in the circle above is 80°, then what is the value of x°+y°  [#permalink]

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11 Sep 2016, 05:33
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35% (medium)

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68% (01:22) correct 32% (01:39) wrong based on 118 sessions

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If arc ABC in the circle above is 80°, then what is the value of x°+y°?

A. 30°
B. 40°
C. 45°
D. 50°
E. 80°

Attachment:

T5315.png [ 9.17 KiB | Viewed 1628 times ]

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Re: If arc ABC in the circle above is 80°, then what is the value of x°+y°  [#permalink]

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11 Sep 2016, 07:02
1
Bunuel wrote:

If arc ABC in the circle above is 80°, then what is the value of x°+y°?

A. 30°
B. 40°
C. 45°
D. 50°
E. 80°

Attachment:
T5315.png

x+y= 1/2 (Arc AB + BC) = 40°

Ans: B
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Re: If arc ABC in the circle above is 80°, then what is the value of x°+y°  [#permalink]

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11 Sep 2016, 07:15
nahid78 wrote:
Bunuel wrote:

If arc ABC in the circle above is 80°, then what is the value of x°+y°?

A. 30°
B. 40°
C. 45°
D. 50°
E. 80°

Attachment:
T5315.png

x+y= 1/2 (Arc AB + BC) = 40°

Ans: B

Hi Nahid78
can you please elaborate how you got

nahid78 wrote:
x+y= 1/2 (Arc AB + BC) = 40°

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If arc ABC in the circle above is 80°, then what is the value of x°+y°  [#permalink]

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11 Sep 2016, 09:32
1
Shrivathsan wrote:
nahid78 wrote:
Bunuel wrote:

If arc ABC in the circle above is 80°, then what is the value of x°+y°?

A. 30°
B. 40°
C. 45°
D. 50°
E. 80°

Attachment:
T5315.png

x+y= 1/2 (Arc AB + BC) = 40°

Ans: B

Hi Nahid78
can you please elaborate how you got

nahid78 wrote:
x+y= 1/2 (Arc AB + BC) = 40°

Angle subtended by the arc at the center is twice the angle subtended at the other end of the circle. So arc ABC could be written as the sum of angle AOB and Angle BOC each as twice angle x and y respectively.
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Re: If arc ABC in the circle above is 80°, then what is the value of x°+y°  [#permalink]

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23 Mar 2017, 09:26
1
Connect point E to point C
Now angle BEC and angle CDB cuts the same arc
As per the rule, if two inscribed angle cuts the same arc then those two angles are same
Therefore angle BEC = angle CDB = y

Now consider the angle AEC=x+y
This angle cuts the arc ABC,
As per the rule, measure of inscribed angle is half the measure of the arc it cuts
Therefore Arc=80
Angle AEC=X+Y=40
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Re: If arc ABC in the circle above is 80°, then what is the value of x°+y°  [#permalink]

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29 Sep 2018, 06:02
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Re: If arc ABC in the circle above is 80°, then what is the value of x°+y°   [#permalink] 29 Sep 2018, 06:02
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