Question

What is mRS? 1000 15x+350 R 9x + 350 X+650 S

Answer 1

You need to remember that there are 360 degrees in a circle. Based on this, you can set up the following equation:

$mUR+mRS+mST+mTU=360\degree$

Knowing that:

$\begin{gathered} mUR=100\degree \\ mRS=9x+35\degree \\ mST=x+65\degree \\ mTS=15x+35\degree \end{gathered}$

You can substitute the expressions into the equation and solve for "x":

$\begin{gathered} 100\degree+(9x+35\degree)+(x+65\degree)+(15x+35\degree)=360\degree \\ \\ 235\degree+25x=360\degree \\ 25x=360\degree-235\degree \\ 25x=125\degree \\ \\ x=\frac{125\degree}{25} \\ \\ x=5\degree \end{gathered}$

Knowing the value of "x", you can find the measure of RS. This is:

$\begin{gathered} mRS=9x+35\degree \\ mRS=9(5\degree)+35\degree \\ mRS=45\degree+35\degree \\ mRS=80\degree \end{gathered}$

The answer is:

$mRS=80\degree$