Question

What is the measure of rst its a pentagon and a nonagon

Answer 1

The sum of measure of exterior angles of a regular polygon is always 360 degree.

Determine the measure of a exterior angle for a regular nonagon.

`\begin{gathered} \angle1=(360)/(9) \\ =40 \end{gathered}`

Determine the measure of exterior angle for a regular pentagon.

`\begin{gathered} \angle2=(360)/(5) \\ =72 \end{gathered}`

The angle RST is equal to sum of exterior angle of nonagon and exterior angle of pentagon. So,

`\begin{gathered} \angle RST=\angle1+\angle2 \\ =72+40 \\ =112 \end{gathered}`

Thus measure of angle RST is 112 degree.