267,665 views
31 votes
31 votes
determine the sum of the measures of the exterior angles of a decagon (ten-sided polygon). question 17 options: a) 1,000° b) 1,800° c) 360° d) 1,440°

User Lasse Edsvik
by
3.4k points

1 Answer

25 votes
25 votes

Answer: c) 360°

Reason:

For any polygon with n sides, the exterior angles always add to 360°

Consider a rectangle where one side is completely horizontal. Place yourself at the bottom right corner. Extending out the bottom side to the right will form a ray pointing directly east. Imagine you are facing along this ray. If you turn 90 degrees to the north, then that is the exterior angle for this vertex.

Now travel north to the upper right corner. Turn 90 degrees west to form the exterior angle. Repeat this 2 more times and you'll have 4 exterior angles of 4*90 = 360 degrees total as the sum of the exterior angle measures. If you traversed around the rectangle, then you'd end up pointing east again after completing the loop. This confirms that you have done a 360 degree full rotation.

This idea can be applied to not only rectangles, but any polygon.

Note: this trick applies to exterior angles only

User Prajna Hegde
by
3.0k points