The greatest angle in a polygon is 110 . Also rests of all angles are distinct in measure. Then the maximum number of sides the polygon can have , is:
Answers
Answer:
The polygon can have maximum no. of sides = 5
Step-by-step explanation:
Since, the greatest angle of the polygon is 110°
Therefore, the exterior angle corresponding to this angle will be minimum
Thus, the exterior angle = 180° - 110° = 70°
All the other angle will be less than this angle
Since, sum of all the exterior angles in a polygon = 360°
Therefore, sum of the rest of the angles = 360° - 70° = 290°
Because all the angles are integers and they are distinct and greater than 70°
The only possibility is that the measures of angles are at minimum
71°, 72°, 73° and 74°
As, 71° + 72° + 73° + 74° = 290°
∵ Total number of exterior angles of the polygon are 5
∴ The maximum sides, the polygon can have is 5
Note: That the angles of the polygons are integers should be there in the question.
5 is the answer , hope it helps u