98.1k views
2 votes
Work out the size of one interior angle of a regular 10 sided shape (decagon)

User Soulfire
by
4.5k points

1 Answer

2 votes

9514 1404 393

Answer:

144°

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

User Colselaw
by
4.8k points