The numerical value of x is 19 and the measure of angle QRS is 53 degrees.
Given that:
Measure of angle PRS = 180 degrees
Measure of angle PRQ = 6x + 13
Measure of angle QRS = 3x - 4
To solve for the measure of angle QRS, first, we need to find the numerical value of x:
Angle PRQ + Angle QRS = Angle PRS
Plug in the values:
6x + 13 + 3x - 4 = 180
Solve for x:
9x + 9 = 180
9x = 180 - 9
9x = 171
x = 171/9
x = 19
Now, we solve for the measure of angle QRS:
Measure of angle QRS = 3x - 4
Plug in x = 19:
Measure of angle QRS = 3(19) - 4
Measure of angle QRS = 57 - 4
Measure of angle QRS = 53 degrees
Therefore, angle QRS measures 53 degrees.