Question

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

Options 106 121 125 127.

Answer 1

we know that

in the triangle PQR

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

In the triangle QSR

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

the answer is

The measure of angle QSR is 27 degrees