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If arc ABC in the circle above is 210°, then what is the value of x°+y

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Bunuel
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If arc ABC in the circle above is 210°, then what is the value of x°+y [#permalink] New post   13 Jul 2021, 01:30
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If arc ABC in the circle above is 210°, then what is the value of x°+y°?

A. 70°
B. 80°
C. 105°
D. 115°
E. 210°

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C
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HarshaBujji
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If arc ABC in the circle above is 210°, then what is the value of x°+y [#permalink] New post   13 Jul 2021, 07:29
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Bunuel wrote:

If arc ABC in the circle above is 210°, then what is the value of x°+y°?

A. 70°
B. 80°
C. 105°
D. 115°
E. 210°


Just construct the below diagram to get more clarity,

Concept: Angle made by the chord at the center is twice that of the angle made by it with any point on the circle.

Hence 2(x+y)=210

So x+y=105

IMO C
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Re: If arc ABC in the circle above is 210°, then what is the value of x°+y [#permalink] New post   13 Jul 2021, 01:38
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Explanation:

As Arc ABC has an angle of 210°
x°+y° will be half of angle Arc ABC i.e. 210/2 = 105°

IMO-C
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Re: If arc ABC in the circle above is 210°, then what is the value of x°+y [#permalink] New post   13 Jul 2021, 02:14
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X is half central angle by arc AB and
Y is half of central angle by arc BC

X+Y = 210/2 = 105

(C) is the right answer

Bunuel wrote:

If arc ABC in the circle above is 210°, then what is the value of x°+y°?

A. 70°
B. 80°
C. 105°
D. 115°
E. 210°

Project PS Butler


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Re: If arc ABC in the circle above is 210°, then what is the value of x°+y [#permalink] New post   13 Jul 2021, 02:48
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If arc ABC in the circle above is 210°

From the above we can see that , 2(x+y) = 210
x+y = 105

IMO C
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Re: If arc ABC in the circle above is 210°, then what is the value of x°+y [#permalink] New post   13 Jul 2021, 05:47
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x + y angle is the angle on the arc ABC (where if we draw AOC where O is center: AOC = 210)
Then x + y = 210/2 = 105 (C)
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If arc ABC in the circle above is 210°, then what is the value of x°+y [#permalink] New post   14 Jul 2021, 00:09
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Bunuel wrote:

If arc ABC in the circle above is 210°, then what is the value of x°+y°?

A. 70°
B. 80°
C. 105°
D. 115°
E. 210°

Project PS Butler


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1.png


Join AOC. Now, you can see that 2(x + y) = 210(Why? Angle made by the chord = 2* angle made by it with any point on the circle)
x + y = 105. (C) IMO!
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If arc ABC in the circle above is 210°, then what is the value of x°+y [#permalink]
14 Jul 2021, 00:09
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