It is given in the question that ray QT bisects ㄥPQR.
[tex]m \angle RQT = (10x - 13), \ and \ m \angle PQT = (6x + 1)[/tex]
And we have to find the measurement of angle PQR.
Since QT bisects angle PQR, therefore measurement of angle RQT and angle PQT are equal. That is
[tex]10x-13=6x+1
\\
4x =14
\\
x = 3.5[/tex]
Substituting the value of x, we will get
[tex]m \angle RQT=10*3.5-13 = 22 degree[/tex]
And measurement of angle PQR is twice of the measurement of angle RQT, that is
[tex]m \angle PQR= 44[/tex]
