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:

1. A heptagon has 7 sides.
2. It has 7 vertices.
3. It has 7 angles.
4. The sum of the interior angles of a heptagon is 900 degrees.
5. The exterior angles of a heptagon add up to 360 degrees.

Formulas for a Heptagon:

To find the sum of the interior angles of a heptagon, you can use the formula:

Sum of interior angles = (n - 2) * 180

where n is the number of sides, so for a heptagon:

Sum of interior angles = (7 - 2) * 180 = 5 * 180 = 900 degrees

The measure of each interior angle of a regular heptagon can be found using the formula:

Measure of each interior angle = Sum of interior angles / Number of sides

For a regular heptagon:

Measure of each interior angle = 900 / 7 ≈ 128.57 degrees

Examples of Heptagons:

Some examples of heptagons in real life include stop signs, certain types of crystals, and some decorative symbols and emblems.

Practice Problems:

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

2. If the measure of one interior angle of a heptagon is 135 degrees, find the measures of the other interior angles.

Conclusion:

A heptagon is a polygon with seven sides and seven angles. Understanding its properties and formulas for calculating its angles can help in solving problems related to heptagons.