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Which of the following is the correct value?
60┬░
30┬░
36┬░
45┬░
36┬░
Remember that the sum of exterior angles of any convex polygon is always 360┬░. For a regular polygon, simply divide 360┬░ by the number of sides n.
We are given a regular decagon, which is a polygon with n = 10 sides.
\text{Exterior Angle} = \frac{360┬░{n}
Remember that the sum of exterior angles of any convex polygon is always 360┬░. For a regular polygon, simply divide 360┬░ by the number of sides n.
Many students confuse the interior angle formula \frac{(n-2) \times 180┬░{n} with the exterior angle formula, often leading to incorrect results.
Identify the number of sides
A decagon is a polygon with n=10 sides.
n=10
Apply the exterior angle formula
The measure of each exterior angle of a regular polygon with n sides is given by dividing the total sum of exterior angles (360┬░) by n.
\text{Exterior Angle} = \frac{360┬░{10}
Calculate the result
Performing the division, we get 360┬░/10=36┬░.
36┬░
C is correct because the exterior angle of a regular decagon is calculated as 360┬░/10=36┬░.
Understanding that the sum of interior and exterior angles at any vertex is 180┬░ (linear pair) allows you to quickly find the interior angle once you have the exterior angle: 180┬░тИТ36┬░=144┬░.
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