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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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New post 19 Mar 2018, 01:53
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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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Re: In a triangle PQR, QS and SR are angle bisectors and the measure of an [#permalink]

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New post 19 Mar 2018, 01:54
Bunuel wrote:
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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


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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 19 Mar 2018, 02:04
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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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New post 19 Mar 2018, 03:31
D is my answer.

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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New post 19 Mar 2018, 05:26
pushpitkc wrote:
Image

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,
Gladi
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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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New post 19 Mar 2018, 05:47
Gladiator59 wrote:
pushpitkc wrote:
Image

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,
Gladi


Hey Gladiator59

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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