Final answer:
To find x, set up an equation using the fact that segment QS is a bisector of angle RQP: x + (3x + 10) = 180. Solve the equation by simplifying and dividing, which gives x = 42.5.
Step-by-step explanation:
To find x, we need to use the fact that segment QS is a bisector of angle RQP. This means that angle RQS and angle PQS are congruent. Since the two angles add up to 180 degrees, we can set up an equation: x + (3x + 10) = 180. Simplifying this equation gives us 4x + 10 = 180. Subtracting 10 from both sides, we get 4x = 170. Finally, dividing both sides by 4 gives us x = 42.5.