Polygons: Convexity, Angles, and Sides

What is the formula to calculate the sum of the interior angles of an 'n' sided polygon?

In a heptagon, how many diagonals can be drawn joining non-adjacent vertices?

For an equilateral triangle, what is the value of each interior angle in degrees?

What is the measure of angle 'w' in a polygon if the exterior angles are 100°, 75°, and 70°?

How many triangles can be formed within a heptagon?

Which term describes a polygon with all angles equal and all sides equal?

What do you call the point at which two sides of a polygon meet?

Which term describes two sides of a polygon that share a common endpoint?

What is the angle formed outside a polygon called?

Polygon Properties and Formulas

The sum of the interior angles of an 'n' sided polygon is calculated using the formula: (n - 2) × 180°.

Heptagon Characteristics

A heptagon has 7 sides, allowing for the drawing of 14 diagonals that connect its non-adjacent vertices.

Equilateral Triangle

An equilateral triangle has all three interior angles equal, each measuring 60°.

Exterior Angles of a Polygon

The measure of angle 'w' in a polygon can be determined by adding the known exterior angles and subtracting from 360°.
For exterior angles of 100°, 75°, and 70°, angle 'w' measures 115° (360° - (100° + 75° + 70°)).

Triangles in a Heptagon

A heptagon can be divided into 5 triangles, illustrating its internal structure.

Definition of a Polygon

A polygon is a closed figure composed of three or more straight line segments, known as sides, which connect at points called vertices.

Regular Polygon

A polygon with all angles and all sides equal is termed a regular polygon.

Vertices and Sides

The point where two sides of a polygon meet is called a vertex.
Two sides of a polygon that share a common endpoint are referred to as adjacent sides.

Exterior Angle Terminology

The angle formed outside a polygon at a vertex is known as an exterior angle.

Learn about convexity, angles, sides of polygons, and how to calculate missing angles in a given polygon. Explore regular polygons with equal angles and sides, as well as irregular polygons. Test your knowledge on shapes like triangle, quadrilateral, pentagon, hexagon, heptagon, octagon, and more!