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# What is the measure of angle SQR in the figure above?

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Math Expert
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What is the measure of angle SQR in the figure above?  [#permalink]

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07 Feb 2018, 05:03
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73% (01:23) correct 27% (01:25) wrong based on 152 sessions

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What is the measure of angle SQR in the figure above?

(1) x = 40°

(2) y = 80°

Attachment:

2018-02-07_1701.png [ 8.74 KiB | Viewed 1573 times ]

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What is the measure of angle SQR in the figure above?  [#permalink]

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07 Feb 2018, 06:19

What is the measure of angle SQR in the figure above?

(1) x = 40°
Knowing the value of x is not enough to find the value of angle SQR unless
we know that the triangles PQS and SQR are congruent.(Insufficient)

(2) y = 80°
If y=80, the angle QSR is 100 degree(sum of angles in a straight line is 180 degree)
Since the angles in a triangle sum up to 180, SQR = 180 - (100+30) = 50(Sufficient - Option B)
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Re: What is the measure of angle SQR in the figure above?  [#permalink]

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07 Feb 2018, 07:30
D

PS=SR --> isosceles triangle.
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What is the measure of angle SQR in the figure above?  [#permalink]

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09 Apr 2020, 05:48
Bunuel wrote:

What is the measure of angle SQR in the figure above?

(1) x = 40°

(2) y = 80°

Attachment:
2018-02-07_1701.png

Bunuel Since PS= SR, isn't the line QS an angle bisector ?
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Re: What is the measure of angle SQR in the figure above?  [#permalink]

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09 Apr 2020, 05:54
sonalchhajed2019 wrote:
Bunuel wrote:

What is the measure of angle SQR in the figure above?

(1) x = 40°

(2) y = 80°

Attachment:
2018-02-07_1701.png

Bunuel Since PS= SR, isn't the line QS an angle bisector ?

We are not given that PS= SR, and you cannot assume that from the figure. Even if we were given that PS= SR, then QS would be median, not an angle bisector.
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Re: What is the measure of angle SQR in the figure above?  [#permalink]

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09 Apr 2020, 08:59
Bunuel wrote:

What is the measure of angle SQR in the figure above?

(1) x = 40°

(2) y = 80°

Attachment:
2018-02-07_1701.png

#1
x=40
insufficient
#2
y=80
angle QSR = 100
and angle SQR = 180-(100+30) ; 50
sufficient
OPTION B
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Re: What is the measure of angle SQR in the figure above?  [#permalink]

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09 Apr 2020, 12:27
Bunuel wrote:
sonalchhajed2019 wrote:
Bunuel wrote:

What is the measure of angle SQR in the figure above?

(1) x = 40°

(2) y = 80°

Attachment:
2018-02-07_1701.png

Bunuel Since PS= SR, isn't the line QS an angle bisector ?

We are not given that PS= SR, and you cannot assume that from the figure. Even if we were given that PS= SR, then QS would be median, not an angle bisector.

But it states it right under the triangle that PS = SR. my reasoning behind A being sufficient is since the PS = SR and angle x is adjacent from PS, won't that make the other angle adjacent to SR equal to angle S?
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Posts: 64248
Re: What is the measure of angle SQR in the figure above?  [#permalink]

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09 Apr 2020, 12:47
1
tomibablo wrote:
Bunuel wrote:
sonalchhajed2019 wrote:

What is the measure of angle SQR in the figure above?

(1) x = 40°

(2) y = 80°

Bunuel Since PS= SR, isn't the line QS an angle bisector ?

We are not given that PS= SR, and you cannot assume that from the figure. Even if we were given that PS= SR, then QS would be median, not an angle bisector.

But it states it right under the triangle that PS = SR. my reasoning behind A being sufficient is since the PS = SR and angle x is adjacent from PS, won't that make the other angle adjacent to SR equal to angle S?

My eyes

Yes. PS = SR but (1) is still not sufficient. For example, consider the image below:
Attachment:

Untitled.png [ 10.73 KiB | Viewed 287 times ]

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Re: What is the measure of angle SQR in the figure above?   [#permalink] 09 Apr 2020, 12:47