what is the sum of the interior angles of the polygon pictured below?

The sum of the interior angles of any polygon depends on the number of sides it has, using the standard formula (n−2)×180∘(n-2)\times 180^\circ (n−2)×180∘, where nnn is the number of sides.

Since the specific polygon pictured below is not visible or described in the query, the exact sum cannot be calculated without knowing nnn (e.g., triangle: 180∘180^\circ 180∘, quadrilateral: 360∘360^\circ 360∘, pentagon: 540∘540^\circ 540∘).

Formula Explanation

This formula derives from dividing the polygon into n−2n-2n−2 triangles, each contributing 180∘180^\circ 180∘. For irregular polygons pictured in problems, count the vertices carefully to apply it.

Common Examples

Polygon| Sides (n)| Sum of Interior Angles
---|---|---
Triangle| 3| 180∘180^\circ 180∘ 1
Quadrilateral| 4| 360∘360^\circ 360∘ 1
Pentagon| 5| 540∘540^\circ 540∘ 1
Hexagon| 6| 720∘720^\circ 720∘ 5

TL;DR: Use(n−2)×180∘(n-2)\times 180^\circ (n−2)×180∘; count sides in the image for the answer.