The given angles mean that line QT divides angle PQS.
The measure of [tex]\angle PQT[/tex] is [tex]15- 3x[/tex]
Given that:
[tex]\angle PQS = 3x + 13[/tex]
[tex]\angle SQT = 6x -2[/tex]
Since QT divides [tex]\angle PQS[/tex];
The equation to calculate [tex]\angle PQT[/tex] is:
[tex]\angle PQT = \angle PQS - \angle SQT[/tex]
This gives
[tex]\angle PQT = 3x + 13- (6x -2)[/tex]
Open bracket
[tex]\angle PQT = 3x + 13- 6x +2[/tex]
Collect like terms
[tex]\angle PQT = 13+2- 6x + 3x[/tex]
[tex]\angle PQT = 15- 3x[/tex]
Hence, the measure of [tex]\angle PQT[/tex] is [tex]15- 3x[/tex]
Read more about angles at:
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