Question

If ray ST bisects ∠VSU, m∠VST = 5x - 3, and m∠VSU = 9x + 3, calculate m∠VST

Answer 1

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:

`9x+3=2(5x-3)`

Let's solve for x.

Apply distributive property to the right side of the equation:

`\begin{gathered} 9x+3=2(5x)+2(-3) \\ \\ 9x+3=10x-6 \end{gathered}`

• Subtract 10x from both sides:

`\begin{gathered} 9x-10x+3=10x-10x-6 \\ \\ -x+3=-6 \end{gathered}`

• Subtract 3 from both sides:

`\begin{gathered} -x+3-3=-6-3 \\ \\ -x=-9 \end{gathered}`

• Divide both sides by -1:

`\begin{gathered} (-x)/(-1)=(-9)/(-1) \\ \\ x=9 \end{gathered}`

Now, to solve for m∠VST, subsitute 9 for x in (5x - 3).

`\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}`

Therefore, the measure of angle VST is 42 degrees.

ANSWER:

42 degrees