In triangle PQR, QS and SR are angle bisectors...

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

In triangle PQR, QS and SR are angle bisectors...

by BTGmoderatorLU » Fri Dec 22, 2017 2:08 pm

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

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

The OA is D.

I'm really confused with this PS question, because I know that in a triangle, the sum of its angles should be 180 degrees, right? But I don't know how can I get the value of ths SQR angle. Experts, any suggestions? Thanks in advanced.

Quote

Source: Beat The GMAT — Problem Solving | Fri Dec 22, 2017 2:08 pm

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Sat Dec 23, 2017 3:25 am

Hello LUANDATO.

Let's take a look at your question.

As QS and RS are bisectors, we can say that PQS=SQR=x and PRS=SRQ=y. Now, we can set the following equation: $$80Âº+x+x+y+y=180Âº\ \Leftrightarrow\ \ 2x+2y=100Âº=x+y=50Âº.$$ Now, if we look at the triangle QSR we can see that $$x+y+QRS=180Âº\ \Leftrightarrow\ \ 50Âº+QRS=180Âº\ \Leftrightarrow\ QRS=130Âº.$$ In conclusion, the correct answer is [spoiler]D=130Âº[/spoiler].

I hope this explanation may help you.

Feel free to ask me again if you have a doubt.

Regards.

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