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505-555 (Easy)|   Geometry|      
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Bunuel
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In a triangle PQR, QS and SR are angle bisectors and the measure of an 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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D
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In a triangle PQR, QS and SR are angle bisectors and the measure of an 19 Mar 2018, 01:54
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Bunuel

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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Attachment:
2018-03-19_1041_001.png
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23. Geometry




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25. Triangles




26. Polygons




27. Circles




28. Rectangular Solids and Cylinders




29. Graphs and Illustrations



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In a triangle PQR, QS and SR are angle bisectors and the measure of an 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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In a triangle PQR, QS and SR are angle bisectors and the measure of an 19 Mar 2018, 03:31
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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 19 Mar 2018, 05:26
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pushpitkc


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)
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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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In a triangle PQR, QS and SR are angle bisectors and the measure of an 19 Mar 2018, 05:47
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Gladiator59
pushpitkc


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
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Hey Gladiator59

Thanks for noticing the typo. I have made the change!
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