Question

What is the measure of RT in the figure below

Answer 1

By symmetry, we can draw the following picture:

`\text{that is}`

arc ST =60 degrees and arc QR=60 degrees. We know that

`\text{arc SQ+arcQR+arcRT+arcST = 360 degr}ees`

and by symmetry, arc SQ is equal to arc RT. By substituting this result and the previous one, we get

`2* arcRT+60+60=360`

which gives

`2* arcRT+120=360`

By moving 120 to the right hand side, we get

`\begin{gathered} 2* arcRT=360-120 \\ 2* arcRT=240 \\ \text{arcRT}=(240)/(2) \end{gathered}`

then, arcRT is equal to 120 degrees