Question

Geometry Question: Find the number of sides an equiangular polygon had if each of its angles is:a.) 144°c.) 156°e.) 172 4/5°

Answer 1

Given:

a) The interior angle in polygon is,

`114^(\circ)`

To find the number of sides,

`\begin{gathered} (360)/(180-\theta)=n \\ n=(360)/(180-144) \\ n=(360)/(36) \\ n=10 \end{gathered}`

Number of sides = 10

c)

`\begin{gathered} \theta=156^(\circ) \\ (360)/(180-\theta)=n \\ n=(360)/(180-156) \\ n=15 \end{gathered}`

Number of sides = 15.

e)

`\begin{gathered} \theta=172(4)/(5)^(\circ) \\ \theta=172^(\circ)+(4)/(5)^(\circ)=172.8^(\circ) \\ (360)/(180-\theta)=n \\ n=\frac{360}{180-172.8^{}} \\ n=(360)/(7.2) \\ n=50 \end{gathered}`

Number of sides = 50