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 x is 2

To find the measure of x, we need to use the fact that angles on the same side of the transversal line PU and between parallel lines QR and ST are supplementary. Therefore, the measure of angle PRQ plus the measure of angle UST must equal
`\( 180^\circ \).`

Given that
`\( PRQ = 120^\circ \)` and
`\( UST = 15(x + 2)^\circ \),` we can set up an equation:

120 + 15(x + 2) = 180

Now, solve for x:

15(x + 2) = 60

Divide both sides by 15:

x + 2 = 4

Subtract 2 from both sides:

x = 2

So, the measure of x is 2