Question

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 120 degrees, and the measure of angle UST is 15 ( x plus 2 ) degrees.

x = 2
x = 6
x = 8
x = 10

Answer 1

The measure of angle PRQ is 120 degrees and the measure of angle UST is 15 (x plus 2) degrees. Since lines QR and ST are parallel, angle PRQ and angle UST are corresponding angles, which means they have the same measure.

Therefore, we can set up the following equation:

120 = 15(x + 2)

Simplifying the equation, we get:

120 = 15x + 30
90 = 15x

Dividing both sides of the equation by 15, we find:

x = 6

Therefore, the measure of x is 6.