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# If O is the center of the circle shown in the figure and angle y is 60

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Math Expert
Joined: 02 Sep 2009
Posts: 52906
If O is the center of the circle shown in the figure and angle y is 60  [#permalink]

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09 Sep 2018, 06:50
00:00

Difficulty:

45% (medium)

Question Stats:

77% (01:26) correct 23% (01:07) wrong based on 18 sessions

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If O is the center of the circle shown in the figure and angle y is 60 degrees, what is the sum of the measures of the angles x + y + z?

A. 150
B. 90
C. 60
D. 30
E. It cannot be determined from the information given.

Attachment:

image039.jpg [ 4.96 KiB | Viewed 420 times ]

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If O is the center of the circle shown in the figure and angle y is 60  [#permalink]

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09 Sep 2018, 07:41
Bunuel wrote:

If O is the center of the circle shown in the figure and angle y is 60 degrees, what is the sum of the measures of the angles x + y + z?

A. 150
B. 90
C. 60
D. 30
E. It cannot be determined from the information given.
Attachment:
The attachment image039.jpg is no longer available

We have, OBC an equilateral triangle (OB=OC=radius, Angle BOC=60, hence Angle OBC=Angle OCB=60 degree)
Note:- The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
So, Angle BAC=$$\frac{60}{2}=30$$

In the triangle ABC, Angle A+Angle B +Angle C=180
Or, 30+x+60+z+60=180
Or, x+y=180-150=30

So, Angle x+y+z=(x+z)+y=30+60=90 degree

Ans. (B)
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circle.png [ 70.41 KiB | Viewed 358 times ]

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If O is the center of the circle shown in the figure and angle y is 60   [#permalink] 09 Sep 2018, 07:41
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