The value of x is 65. Please note that this solution is based on the assumption that the angles QRP and PSQ are supplementary. If this assumption doesn't hold, feel free to let me know.
We need to find the value of x in the equation ZQRP = (2x + 20)° given that ZPSQ = 30°. Since the question doesn't provide enough information about the relationship between angles QRP and PSQ, I'll assume that they are supplementary angles (angles that add up to 180°). This assumption is based on the possibility that the angles form a straight line or a linear pair.
If angles QRP and PSQ are supplementary, their sum is 180°:
(2x + 20)° + 30° = 180°
Now, we can solve for x:
2x + 50 = 180
Subtract 50 from both sides:
2x = 130
Divide by 2:
x = 65