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

$2\times arcRT+60+60=360$

which gives

$2\times arcRT+120=360$

By moving 120 to the right hand side, we get

$\begin{gathered} 2\times arcRT=360-120 \\ 2\times arcRT=240 \\ \text{arcRT}=\frac{240}{2} \end{gathered}$

then, arcRT is equal to 120 degrees