find the measure of an interior angle of a regular polygon of 9 sides
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Answer:
The answer is
Step-by-step explanation:
An interior angle of a regular polygon can be found by using the formula
[tex] \frac{(n - 2) \times 180}{n} [/tex]
where
n is the number of sides of the polygon
From the question the polygon has 9 sides that's n = 9
Substitute this value into the above formula and solve
We have
[tex] \frac{(9 - 2) \times 180}{9} \\ \rarr \: \frac{7 \times 180}{9} \\ \rarr \: \frac{1260}{9} \: \: \: \: \: \: [/tex]
We have the final answer as
Hope this helps you
We know that, the sum of all angles of a polygon can be calculated by:
[tex](n - 2) \times 180 \degree[/tex]
But in case of regular polygon, all the angles are equal. So, the measure of each angle can be found by dividing it by number of sides i.e n.
So, Value of each angle:
[tex] \dfrac{(n - 2) \times 180 \degree}{n} [/tex]
Given
By using formula,
Measure of each interior angle:
[tex] \dfrac{(9 - 2) \times 180 \degree}{9}[/tex]
[tex] \dfrac{7 \times 180 \degree}{9} [/tex]
[tex]7 \times 20 \degree[/tex]
[tex] \boxed{ \red{ \bf{140 \degree}}}[/tex]
So, measure of each angle = 140°
And we are done !!
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