Given:
a) The interior angle in polygon is,
[tex]114^{\circ}[/tex]
To find the number of sides,
[tex]\begin{gathered} \frac{360}{180-\theta}=n \\ n=\frac{360}{180-144} \\ n=\frac{360}{36} \\ n=10 \end{gathered}[/tex]
Number of sides = 10
c)
[tex]\begin{gathered} \theta=156^{\circ} \\ \frac{360}{180-\theta}=n \\ n=\frac{360}{180-156} \\ n=15 \end{gathered}[/tex]
Number of sides = 15.
e)
[tex]\begin{gathered} \theta=172\frac{4}{5}^{\circ} \\ \theta=172^{\circ}+\frac{4}{5}^{\circ}=172.8^{\circ} \\ \frac{360}{180-\theta}=n \\ n=\frac{360}{180-172.8^{}} \\ n=\frac{360}{7.2} \\ n=50 \end{gathered}[/tex]
Number of sides = 50
