Solve for Interior Angles Calculator

Interior Angle Formula:

\[ \text{Interior Angle} = 180° - \text{Exterior Angle} \] \[ \text{Regular Polygon Interior Angle} = \frac{(n-2) \times 180°}{n} \]

Calculation Type:

Exterior Angle:

degrees

Number of Sides:

sides

Interior Angle:

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1. What are Interior Angles?

An interior angle is an angle formed inside a polygon at one of its vertices. For regular polygons (where all sides and angles are equal), interior angles can be calculated using a simple formula based on the number of sides.

2. How to Calculate Interior Angles

There are two main ways to calculate interior angles:

From Exterior Angle: \[ \text{Interior Angle} = 180° - \text{Exterior Angle} \]

From Number of Sides (Regular Polygon): \[ \text{Interior Angle} = \frac{(n-2) \times 180°}{n} \]

Where:

\( n \) — Number of sides in the regular polygon
Exterior Angle — Angle formed outside the polygon at a vertex

3. Importance of Interior Angles

Details: Interior angles are fundamental in geometry, used in polygon analysis, architectural design, and various engineering applications. They help determine the shape and properties of polygons.

4. Using the Calculator

Tips: Select whether you want to calculate from exterior angle or number of sides. Enter the appropriate value (exterior angle between 0-180° or number of sides ≥3).

5. Frequently Asked Questions (FAQ)

Q1: What's the sum of interior angles in a polygon?
A: The sum is (n-2) × 180°, where n is the number of sides.

Q2: What's the interior angle of a regular pentagon?
A: For a pentagon (5 sides), each interior angle is 108°.

Q3: Can I use this for irregular polygons?
A: The calculator works for regular polygons. For irregular polygons, interior angles vary and must be measured individually.

Q4: What's the relationship between interior and exterior angles?
A: They are supplementary - they add up to 180° at each vertex.

Q5: What's the smallest possible interior angle?
A: For a regular polygon, the smallest interior angle is 60° (equilateral triangle). As sides increase, interior angles approach 180°.