Math Problem Statement

Calculate the total of the interior angles of this heptagon.

Solution

To calculate the total of the interior angles of a heptagon (7-sided polygon), we use the given formula:

T=180×(n2)T = 180^\circ \times (n - 2)

where TT is the total sum of the interior angles, and nn is the number of sides of the polygon. For a heptagon, n=7n = 7.

Substitute n=7n = 7 into the formula:

T=180×(72)T = 180^\circ \times (7 - 2) T=180×5T = 180^\circ \times 5 T=900T = 900^\circ

Thus, the total sum of the interior angles of the heptagon is 900°.

Would you like more details or have any questions?

Here are 5 related questions for further practice:

  1. What is the sum of the interior angles of a hexagon (6-sided polygon)?
  2. How do you calculate the measure of one interior angle in a regular polygon?
  3. What is the total of the exterior angles of any polygon?
  4. What is the relationship between the number of sides of a polygon and its interior angles?
  5. How do the interior and exterior angles of a polygon add up at each vertex?

Tip: The sum of the exterior angles of any polygon is always 360°, regardless of the number of sides!

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Math Problem Analysis

Mathematical Concepts

Geometry
Polygons
Interior Angles

Formulas

T = 180° × (n - 2)

Theorems

Sum of Interior Angles Theorem

Suitable Grade Level

Grades 6-8