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505-555 (Easy)|   Geometry|      
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Asifpirlo
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In triangle PQR, QS and SR are angle bisectors and the measu 24 Aug 2013, 15:58
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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15% (low)

Question Stats:

86% (01:22) correct 14% (01:51) wrong based on 106 sessions

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tria.png [ 3.48 KiB | Viewed 29859 times ]
In triangle PQR, QS and SR are angle bisectors and the measure of angle P = 80°. How many degrees are there in angle QSR ?

(A) 115º
(B) 120º
(C) 125º
(D) 130º
(E) 135º
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D
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Bunuel
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In triangle PQR, QS and SR are angle bisectors and the measu 25 Aug 2013, 06:11
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In triangle PQR, QS and SR are angle bisectors and the measure of angle P = 80°. How many degrees are there in angle QSR ?

(A) 115º
(B) 120º
(C) 125º
(D) 130º
(E) 135º

<Q + <R = 180 - 80 = 100;

Q/2 + R/2 = 50 --> angle QSR = 180 - 50 = 130.

Answer: D.
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In triangle PQR, QS and SR are angle bisectors and the measu 25 Aug 2013, 15:26
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Bunuel

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

(A) 115º
(B) 120º
(C) 125º
(D) 130º
(E) 135º

<Q + <S = 180 - 80 = 100;

Q/2 + S/2 = 50 --> angle QSR = 180 - 50 = 130.

Answer: D.
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really sweet solution of a sweet PS............... :)
Thanks Boss
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In triangle PQR, QS and SR are angle bisectors and the measu 02 Mar 2015, 06:05
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Bunuel

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

(A) 115º
(B) 120º
(C) 125º
(D) 130º
(E) 135º

<Q + <S = 180 - 80 = 100;

Q/2 + S/2 = 50 --> angle QSR = 180 - 50 = 130.

Answer: D.
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Bunuel - what throws me off in this question is that I have trouble with the actual visual image. When I initially saw it I froze because QS isn't perpendicular or even connecting to PR so I didn't even think about possibly doing 180 - 80 to get <Q + <S. I viewed the possible angles as I have highlighted in the photo https://pho.to/8whO9
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In triangle PQR, QS and SR are angle bisectors and the measu 07 May 2015, 02:55
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Bunuel

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

(A) 115º
(B) 120º
(C) 125º
(D) 130º
(E) 135º

<Q + <S = 180 - 80 = 100;

Q/2 + S/2 = 50 --> angle QSR = 180 - 50 = 130.

Answer: D.
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Bunuel:

I have not understood, how you have arrived to <Q + <S = 180 - 80 = 100;
Please explain.
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In triangle PQR, QS and SR are angle bisectors and the measu 07 May 2015, 03:02
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Bunuel

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

(A) 115º
(B) 120º
(C) 125º
(D) 130º
(E) 135º

<Q + <S = 180 - 80 = 100;

Q/2 + S/2 = 50 --> angle QSR = 180 - 50 = 130.

Answer: D.

Bunuel:

I have not understood, how you have arrived to <Q + <S = 180 - 80 = 100;
Please explain.
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There was a typo. It's:
<Q + <R = 180 - 80 = 100;

Q/2 + R/2 = 50 --> angle QSR = 180 - 50 = 130.

Answer: D.
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In triangle PQR, QS and SR are angle bisectors and the measu 26 Jul 2015, 12:22
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Hi Bunuel,

Why have u taken Q/2+R/2= 50. Can u please throw some light.

Thanks!
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In triangle PQR, QS and SR are angle bisectors and the measu 26 Jul 2015, 12:37
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sharmarahul12
Hi Bunuel,

Why have u taken Q/2+R/2= 50. Can u please throw some light.

Thanks!
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Q/2 and R/2 have been taken as QS and RS are angle bisectors (= divide angles PQR and PRQ each into 2 equal angles).

This means <SQR = <PQS = x.....(1) and <PRS = <SRQ = y .....(2)

Thus, from triangle PQR

<P + <Q +<R = 180 ---> 80+<Q+<R = 180 ---> <Q+<R =100 ---> From (1) and (2) above, 2x+2y = 100 ---> x+y =50 (this is same as Q/2 +R/2 = 50)

Now, in triangle SQR ,

<QSR + <SQR + <SRQ = 180 ---> <QSR +x + y = 180 --> <QSR = 180-50=130. D is the correct answer.
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In triangle PQR, QS and SR are angle bisectors and the measu 07 Mar 2022, 07:45
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