How many sides does a polygon have if the sum of the measures of its interior angles is 540
Answers
Answer:
The figure will be Pentagon with 5 sides
Step-by-step explanation:
hopefully it helps ❤️
Mark me brainliest ❤️
Answer:
n = 5
There are 5 sides of the polygon, that is, it is a pentagon.
Step-by-step explanation:
From one vertex of n sided polygon, we can draw (n-3) diagonals. This is because the two adjacent vertices form adjacent sides and not diagonals. So, from the n number of vertices, one is the vertex itself from where we are drawing the diagonals, and we have just discussed about the two adjacent vertices.
With n - 3 diagonals from one vertex, we will get (n - 2) triangles dividing all the interior angles of the n sided polygon amongst themselves.
Therefore, the sum of the interior angles of n sided regular polygon is (n - 2)x180°
According to the problem:
(n - 2)x180° = 540° = 3x180°
∴ n - 2 = 3
∴ n = 3 + 2 = 5
∴ There are 5 sides of the polygon, that is, it is a pentagon.