Heptagon

A heptagon is a polygon with seven sides and seven angles. The sum of the interior angles of a heptagon is always 900 degrees.

Properties of a Heptagon:

• A heptagon has 7 sides and 7 angles.
• The sum of the interior angles of a heptagon is 900 degrees.
• All the interior angles of a regular heptagon are congruent.
• The exterior angles of a heptagon add up to 360 degrees.
• A heptagon has 14 diagonals.

Formulas for a Heptagon:

• Sum of Interior Angles: (n-2) * 180 degrees, where n is the number of sides.
• Each Interior Angle: (n-2) * 180 / n degrees, where n is the number of sides.
• Sum of Exterior Angles: 360 degrees.
• Number of Diagonals: n * (n-3) / 2, where n is the number of sides.

Example Problems:

1. Find the measure of each interior angle of a regular heptagon.

Each Interior Angle: (7-2) * 180 / 7 = 900 / 7 = 128.57 degrees

2. Calculate the sum of the interior angles of a heptagon.

Sum of Interior Angles: (7-2) * 180 = 5 * 180 = 900 degrees

Practice Questions:

1. Find the measure of each interior angle of a regular heptagon.
2. Calculate the sum of the interior angles of a heptagon.
3. Find the number of diagonals in a heptagon.

Now you have a good understanding of heptagons and are ready to solve problems related to them!