Answer:
The polygon has 10 sides
Step-by-step explanation:
One of the interior angles of a polygon can be found using the formula
[tex] \frac{(n - 2) \times180\degree }{n} [/tex]
where n is the number of sides of the polygon
From the question
One of the interior angles = 144
To find the number of sides substitute this value into the above formula and solve for n
That's
[tex]144 = \frac{(n - 2) \times 180}{n} [/tex]
Cross multiply
We have
[tex]144n = (n - 2) \times 180[/tex]
Expand the terms in the bracket
[tex]144n = 180n - 360[/tex]
Group like terms
[tex]144n - 180n = - 360 \\ \\ - 36n = - 360[/tex]
Divide both sides by - 36
That's
[tex] \frac{ - 36n}{ - 36} = \frac{ - 360}{ - 36} [/tex]
We have the final answer as
n = 10 sides
Hope this helps you
