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Goryan [66]
3 years ago
5

In triangle PQR, Line QS and line SR are angle bisectors to angle P (74 degrees). How many Degrees are in the angle QSR.

Mathematics
1 answer:
AlexFokin [52]3 years ago
4 0

we know that

<u>in the triangle PQR</u>

m∠PQR+m∠QPR+m∠QRP=180°------> the sum of the internal angles of a triangle is equal to 180 degrees

(m∠PQR+m∠QRP)+74°=180°-------> (m∠PQR+m∠QRP)=106°

we know that

If QS and SR are angle bisectors

then

<u>In the triangle QSR</u>

m∠SQR+m∠QSR+m∠QRS=180°-------> equation 1

and

(m∠SQR+m∠QRS)=106°/2--------> (m∠SQR+m∠QRS)=53°

substitute the value of (m∠SQR+m∠QRS)=53° in the equation 1

53°+m∠QSR=180°

m∠QSR=180°-53°-------->m∠QSR= 27°

therefore

<u>the answer is</u>

The measure of angle QSR is  27 degrees

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