The second way to check if a polygon is a concave polygon is to look at the diagonals of the polygon.
If one or more diagonals are located outside or partly outside of the polygon, then the polygon is a concave polygon.
The polygon above has 5 diagonals made with dotted lines.
Three of them are completely inside and these are the green, orange, and teal dotted lines.
One is completely outside and it is red dotted line.
One is partially outside and it is the black dotted line.
The polygon is not a concave polygon because of the followings two situations occur.
1. Four interior angles of an irregular pentagon measure 68, 176, 90 and 126. Is the irregular pentagon a concave pentagon?
Solution
We just need to find the measure of the last angle to see if it is bigger than 180 degrees. The sum of the interior angles in a pentagon is 540.
68 + 176 + 90 + 126 + x = 540
460 + x = 540
x = 540  460 = 80
Since none of the angles inside the pentagon measure more than 180, the pentagon is not a concave pentagon.
2. Three interior angles of a quadrilateral measure 50, 105, and 15. Is the quadrilateral a concave quadrilateral?
Solution
We just need to find the measure of the last angle to see if it is bigger than 180 degrees. The sum of the interior angles in a quadrilateral is 360.
50 + 105 + 15 + x = 360
170 + x = 360
x = 360  170 = 190
Since one angle inside the quadrilateral measure more than 180, the quadrilateral is a concave quadrilateral.

May 07, 21 02:29 PM
A timeseries data shows information about the same subject or element of a sample or population for different periods of time.
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