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

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

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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

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.

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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: $$80º+x+x+y+y=180º\ \Leftrightarrow\ \ 2x+2y=100º=x+y=50º.$$ Now, if we look at the triangle QSR we can see that $$x+y+QRS=180º\ \Leftrightarrow\ \ 50º+QRS=180º\ \Leftrightarrow\ QRS=130º.$$ In conclusion, the correct answer is D=130º.

I hope this explanation may help you.

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

Regards.

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