The figure above shows a regular 9-sides polygon. What is the value of X ?

Insert the value


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Thank you to point out. I had a mismatch posting the question.

yes, it is true. It is 40. Thank you once again.

regards
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isnt 360/n a simpler solution? 360/9=40

Points to remember:-

Sum of Interior Angles = (n-2) × 180° (n = number of sides)

Each Angle (of a Regular Polygon) = \(\frac{(n-2) * 180}{n}\)
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Useful rule: the sum of the angles in an n-sided polygon = (n - 2)(180°)

So, the sum of the angles in an 9-sided polygon = (9 - 2)(180°) = 1260°

Since we have a REGULAR 9-sides polygon, each interior angle is EQUAL
1260°/9 = 140°
So, each interior angle is 140°


We get:



Since one of the 140° lies on the same line as angle x we know that the two angles add to 180°

We get" x° + 140° = 180°
Solve: x = 40°

Answer: 40

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

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