Given:
QR and ST are parallel lines, and PU is a transversal line.
[tex]m\angle TSU=15(x+2)[/tex]
[tex]m\angle PRQ=135^\circ[/tex]
To find:
The value of x.
Solution:
If a transversal line intersect two parallel lines, then the alternate exterior angles are equal.
[tex]m\angle TSU=m\angle PRQ[/tex] (Alternate exterior angles)
[tex]15(x+2)=135[/tex]
[tex]15x+30=135[/tex]
Subtracting 30 from both sides, we get
[tex]15x=135-30[/tex]
[tex]15x=105[/tex]
Dividing both sides, we get 15.
[tex]\dfrac{15x}{15}=\dfrac{105}{15}[/tex]
[tex]x=7[/tex]
Therefore, the value of x is 7.
