Given:
• Ray ST bisects ∠VSU
,• m∠VST = (5x - 3) degrees
,• m∠VSU = (9x + 3) degrees
Let;s solve for m∠VST.
Let's first sketch a figure which represents this situation:
Since ST bisects angle VSU, it means ST divides angle VSU exactly by half.
Thus, we have:
m∠VST = m∠TSU
m∠VSU = m∠VST + m∠TSU
m∠VSU = 2(m∠VST)
Now, input the terms into the equation:
[tex]9x+3=2(5x-3)[/tex]Let's solve for x.
Apply distributive property to the right side of the equation:
[tex]\begin{gathered} 9x+3=2(5x)+2(-3) \\ \\ 9x+3=10x-6 \end{gathered}[/tex]• Subtract 10x from both sides:
[tex]\begin{gathered} 9x-10x+3=10x-10x-6 \\ \\ -x+3=-6 \end{gathered}[/tex]• Subtract 3 from both sides:
[tex]\begin{gathered} -x+3-3=-6-3 \\ \\ -x=-9 \end{gathered}[/tex]• Divide both sides by -1:
[tex]\begin{gathered} \frac{-x}{-1}=\frac{-9}{-1} \\ \\ x=9 \end{gathered}[/tex]Now, to solve for m∠VST, subsitute 9 for x in (5x - 3).
[tex]\begin{gathered} m\angle VST=5x-3 \\ \\ m\angle VST=5(9)-3 \\ \\ m\angle VST=45-3 \\ \\ m\angle VST=42^o \end{gathered}[/tex]Therefore, the measure of angle VST is 42 degrees.
ANSWER:
42 degrees
