Question

What ever I'm doing is making the circle equal 410 degrees.

Answer 1

Step 1

Redraw the cyclic quadrilateral

From the image;

`\begin{gathered} mSTU=220 \\ \text{mSRU}=360\text{ -220=110(sum of angles at a point or in a circle is 3}60^o) \end{gathered}`

Step 2

Find the measure of angle R

`m\angle R=(1)/(2)mSTU`

`m\angle R=(1)/(2)*220=110`

Find the measure of angle T

`\begin{gathered} m\angle T=(1)/(2)mSRU \\ m\angle T=(1)/(2)*140 \\ m\angle T=70 \end{gathered}`

Find the measure of angle U

`m\angle U=360-95-110-70=85\text{ ( sum of angles in quadrilateral)}`

Find the measure of Arc SRU

`\begin{gathered} \text{mSRU}=\text{ }360-\text{mSTU} \\ \text{mSRU}=360-220=140 \end{gathered}`

Find the measure of Arc mRUT

`\begin{gathered} \text{mRUT}=\text{ 2}* m\angle S \\ \text{mRUT}=2*95=190 \end{gathered}`

Find the measure of mRST

`\begin{gathered} \text{mRST}=2* m\angle U \\ \text{mRST}=2*85=170 \end{gathered}`