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.

$\begin{gathered} \angle1=\frac{360}{9} \\ =40 \end{gathered}$

Determine the measure of exterior angle for a regular pentagon.

$\begin{gathered} \angle2=\frac{360}{5} \\ =72 \end{gathered}$

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.