Given a n-sided regular polygon and three vertices a1, a2 and a3, the task is to find the angle suspended at vertex a1 by vertex a2 and vertex a3.
Input: n = 6, a1 = 1, a2 = 2, a3 = 4 Output: 90 Input: n = 5, a1 = 1, a2 = 2, a3 = 5 Output: 36
- The angle subtended by an edge on the center of n sided regular polygon is 360/n.
- The angle subtended by vertices seperated by k edges becomes (360*k)/n.
- The chord between the vertices subtends an angle with half the value of the angle subtended at the center at the third vertex which is a point on the circumference on the circumcircle.
- Let the angle obtained in this manner be a = (180*x)/n where k is number of edges between i and k.
- Similarily for the opposite vertex we get the angle to be b = (180*y)/n where l is number of edges between j and k.
- The angle between the three vertices thus equals 180-a-b.
Below is the implementation of the above approach:
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