Work out the size of one interior angle of a regular 10 sided shape (decagon)

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05-05-2021
Mathematics

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Work out the size of one interior angle of a regular 10 sided shape (decagon)

Sagot :

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Sqdancefanidn Sqdancefanidn · Answer 1 · 2021-05-10T14:42:37-04:00

9514 1404 393

Answer:

144°

Step-by-step explanation:

The interior angle of a polygon is the supplement of the exterior angle at that vertex. The sum of exterior angles of a convex polygon is always 360°.

The exterior angle at each vertex of a regular decagon will be 360°/10 = 36°. Then the interior angle is ...

180° -36° = 144° . . . . measure of regular decagon interior angle

_____

Interior angle A of an n-sided polygon has the measure ...

A = 180° -360°/n = 180°(n -2)/n

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