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# In a triangle PQR, QS and SR are angle bisectors and the measure of an

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In a triangle PQR, QS and SR are angle bisectors and the measure of an  [#permalink]

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19 Mar 2018, 01:53
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15% (low)

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89% (01:06) correct 11% (02:23) wrong based on 39 sessions

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In a triangle PQR, QS and SR are angle bisectors and the measure of angle P = 80°. How many degrees are there in angle QSR?

A. 115°
B. 120°
C. 125°
D. 130°
E. 135°

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2018-03-19_1041_001.png [ 8.07 KiB | Viewed 1470 times ]

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Re: In a triangle PQR, QS and SR are angle bisectors and the measure of an  [#permalink]

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19 Mar 2018, 01:54
Bunuel wrote:

In a triangle PQR, QS and SR are angle bisectors and the measure of angle P = 80°. How many degrees are there in angle QSR?

A. 115°
B. 120°
C. 125°
D. 130°
E. 135°

Attachment:
2018-03-19_1041_001.png

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In a triangle PQR, QS and SR are angle bisectors and the measure of an  [#permalink]

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19 Mar 2018, 02:04

In Triangle PQR, 80 + Q + R = 180
Here, Q + R = 180 - 80 = 100

As SQ and SR are angle bisectors, the angle Q and R will be equally divided '
on both sides. If the angles of the triangle SQR and x and y,

x + y is half of the sum of Q and R, which is $$\frac{100°}{2} = 50$$°

Therefore, the measure of angles QSR = 180° - 50° = 130° (Option D)
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Re: In a triangle PQR, QS and SR are angle bisectors and the measure of an  [#permalink]

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19 Mar 2018, 03:31

although the question doesnt mention that the bigger triangle is isosceles.. i have assumed it to be isosceles.
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In a triangle PQR, QS and SR are angle bisectors and the measure of an  [#permalink]

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19 Mar 2018, 05:26
pushpitkc wrote:

In Triangle PQR, 80 + Q + R = 180
Here, Q + R = 180 - 80 = 100

As SQ and QR are angle bisectors, the angle Q and R will be equally divided '
on both sides. If the angles of the triangle SQR and x and y,

x + y is half of the sum of Q and R, which is $$\frac{100°}{2} = 50$$°

Therefore, the measure of angles QSR = 180° - 50° = 130° (Option D)

Hi pushpitkc,
SR is the angle bisector and not QR. I think it is a typo .

Hi himanshutonu,

You do not need to assume the larger triangle to be isoceles. We do not need the two angle to be equal for their angle bisectors to make angles x + y = 1/2 ( sum of original angle ). This is true for all triangles and not only isoceles.

This is evident from the quoted explanation by pushpitkc.

Best,
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Re: In a triangle PQR, QS and SR are angle bisectors and the measure of an  [#permalink]

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19 Mar 2018, 05:47
pushpitkc wrote:

In Triangle PQR, 80 + Q + R = 180
Here, Q + R = 180 - 80 = 100

As SQ and QR are angle bisectors, the angle Q and R will be equally divided '
on both sides. If the angles of the triangle SQR and x and y,

x + y is half of the sum of Q and R, which is $$\frac{100°}{2} = 50$$°

Therefore, the measure of angles QSR = 180° - 50° = 130° (Option D)

Hi pushpitkc,
SR is the angle bisector and not QR. I think it is a typo .

Hi himanshutonu,

You do not need to assume the larger triangle to be isosceles. We do not need the two angle to be equal for their angle bisectors to make angles x + y = 1/2 ( sum of original angle ). This is true for all triangles and not only isoceles.

This is evident from the quoted explanation by pushpitkc.

Best,

Thanks for noticing the typo. I have made the change!
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Re: In a triangle PQR, QS and SR are angle bisectors and the measure of an   [#permalink] 19 Mar 2018, 05:47
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