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Each exterior angle measures 10 degrees

Each interior angle measures 170 degrees

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Q: What is the measure of an angle in a regular 36 gon?

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It is: 360/36 = 10 sided regular decagon polygon

Exterior Angle for a decagon is 36 Degrees.

36 gon

The total degree measure in a decagon is 180(8) since a decagon can be broken up into 8 triangles. In a regular decagon, each angle has the same measure: 180(8)/10=18(8)=144. The supplementary angle, 36, is therefore the angle between the side bc and (each of) the two extended sides ab, CD outside of the decagon. The remaining angle, k, of the triangle thus formed is 180-2(36)=180-72=108. A sneaky way to get the same answer is to notice that if we extend every other side of the regular decagon, we get a (larger) regular pentagon. The angle k is one of these angles, so it is 108.

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36

170 degrees

360/36 = 10 degrees

Each exterior angle measures 36 degrees Each interior angle measures 144 degrees

360/36 = 10 degrees

The exterior angles of any polygon add up to 360 degrees. So: 360/10 = 36 degrees

Each interior angle of a 36-gon measures 170 degrees. In general, if you have a regular n-gon, it's interior angles will measure (n-2)*180/n degrees. This is due to the fact that if we choose a single vertex from the regular n-gon and draw all possible diagonals to all of the other vertices there will be n-2 triangles inside the regular n-gon. Each of these triangles has a total of 180 degrees. Thus, there are (n-2)*180 degrees divided among the n vertices.

36

Providing that it's a regular decagon then each exterior angle will measure 36 degrees

Providing that it's a regular decagon then each exterior angle will measure 36 degrees

36

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