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
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