Question

what will be the angle-sum of a convex polygon with 7 sides?

Answer 1

Answer:

5 × 180° = 900°

Step-by-step explanation:

The sum of the internal angles of a convex polygon with n sides is (n-2)×180°.

To see why, pick a vertex and draw lines from there to the other vertices.  This cuts the polygon into n-2 triangles.  The sum of the internal angles of the polygon is then just the sum of the angles in these triangles, so we get (n-2)×180°.

For this question, we have n = 7, so the sum of the angles is:

(7-2) × 180° = 5 × 180° = 900°.

Answer 2

Answer:

The sum of all angles of a seven sided convex polygon is found to be: $900^\circ$.

Step-by-step explanation:

• In geometry, a convex polygon is a polygon that represents the boundaries of a convex set. This means that the line segment between the two points of the polygon is included in the connection between the inside and the boundary of the polygon. Specifically, it's a simple polygon (not a self-intersection). Similarly, if all lines without edges intersect the polygon  at up to two points, the polygon will be convex.
• Strictly a convex polygon is with no lines containing two edges. All internal angles of  a convex polygon are less than 180 degrees, but exactly all internal angles of a convex polygon  are less than 180 degrees.
• Also, we know that the expression for finding the sum of all angles in a 'n'-sided convex polygon is given by:
  $Angle\ =\ (n-2)\times180^\circ$
            $=(7-2)\times 180^\circ\\=5\times180^\circ\\=900^\circ$
  Thus, the angle sum is found to be $900^\circ$.

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