Answer:
Part 1) x=8
Part 2) m∠RSU=133°
Part 3) m∠UST=47°
Part 4) m∠WSV=43°
Part 5) m∠VSU=137°
Step-by-step explanation:
see the attached figure to better understand the problem
Part 1) Find the value of x
we know that
m∠RSU and m∠UST are supplementary angles (by linear pair)
so
m∠RSU+m∠UST=180°
we have
m∠RSU=(17x-3)°
m∠UST=(6x-1)°
substitute the given values and solve for x
[tex](17x-3)\°+(6x-1)\°=180\°[/tex]
[tex](23x-4)=180[/tex]
[tex]23x=180+4[/tex]
[tex]23x=184[/tex]
[tex]x=8[/tex]
Part 2) Find the measure of m∠RSU
we have
m∠RSU=(17x-3)°
substitute the value of x
m∠RSU=17(8)-3=133°
Part 3) Find the measure of m∠UST
we have
m∠UST=(6x-1)°
substitute the value of x
m∠UST=6(8)-1=47°
Part 4) Find the measure of m∠WSV
we know that
m∠UST=m∠RSW -----> by vertical angles
so
m∠RSW=47°
m∠RSW+m∠WSV=90° ----> given problem (SV perpendicular RT)
substitute the value of m∠RSW and solve for m∠WSV
47°+m∠WSV=90°
m∠WSV=90°-47°=43°
Part 5) Find the measure of m∠VSU
we know that
m∠VSU=m∠VST+m∠UST
we have
m∠VST=90° ----> given problem (SV perpendicular RT)
m∠UST=47°
substitute
m∠VSU=90°+47°=137°
