Find the measure of x.
Line PU has points R and S between points P and U, lines QR and ST are parallel, line QR intersects line PU at point R, line ST intersects line PU at point S, the measure of angle PRQ is 150, and the measure of angle UST is 15 ( x plus 1 ).
x = 1
x = 9
x = 10
x = 11
To find the measure of x, we can use the fact that alternate interior angles are congruent when two parallel lines are intersected by a transversal.
Since lines QR and ST are parallel, we can conclude that angle RQS is also 150 degrees.
Now, we can use the fact that the sum of angles in a triangle is 180 degrees.
In triangle PQS, we have angle PQS + angle PSQ + angle QSP = 180.
Substituting the given angles, we have:
150 + 150 + (x + 1) = 180.
Now we can solve for x:
300 + x + 1 = 180.
x + 301 = 180.
x = 180 - 301.
x = -121.
Therefore, none of the given options (1, 9, 10, 11) for x are correct.