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 135 degrees, and the measure of angle UST is 15 open parenthesis x plus 2 close parenthesis degrees. x

Answer 1

The value of x is 1.

* Let's explain how to solve the problem

- Line PU has points R and S between points P and U

- Line QR intersects line PU at point R

- Line ST intersects line PU at point S

- Lines QR and ST are parallel

- Look to the attached figure

∵ QR // ST

∴ m∠TSU = m∠QRU ⇒ corresponding angles

∵ m∠TSU = 15(x + 2)°

∴ m∠QRU = 15(x + 2)

∵ Points P, R, S lie on the same line

∵ RQ intersects PS at R

∵ m∠PRQ + m∠QRU = 180° ⇒ straight angle

∵ m∠PRQ = 135°

∵ m∠QRU = 15(x + 2)°

∴ 135 + 15(x + 2) = 180

∴ 135 + 15x + 30 = 180

- Add like terms

∴ 15x + 165 = 180

- Subtract 165 from both sides

∴ 15x = 15

- Divide both sides by 15

∴ x = 1

∴ The value of x is 1

In geometry, parallel lines are coplanar instantly traces that do not intersect at any factor. Parallel planes are planes in identical three-dimensional space that in no way meet. Parallel curves are curves that do not touch every different or intersect and hold a set minimal distance

In mathematics, the intersection of or more gadgets is any other item that includes the whole thing that is contained in all the items simultaneously.

Learn more about parallel lines here : brainly.com/question/24756209

#SPJ4