How To Calculate Exterior Angle

Exterior Angle Formula:

\[ \text{Exterior Angle} = \sum \text{Interior Angles} - 180^\circ \]

Exterior Angle:

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1. What is an Exterior Angle?

An exterior angle of a triangle is formed when one side of the triangle is extended. It is equal to the sum of the two opposite interior angles. For any triangle, the exterior angle can be calculated using the formula: Exterior Angle = Sum of Interior Angles - 180°.

2. How Does the Calculator Work?

The calculator uses the exterior angle formula:

\[ \text{Exterior Angle} = \sum \text{Interior Angles} - 180^\circ \]

Where:

\( \sum \text{Interior Angles} \) — Sum of all interior angles of the triangle (degrees)
\( 180^\circ \) — Total degrees in a straight line

Explanation: Since the sum of interior angles in any triangle is always 180°, this formula calculates the exterior angle by subtracting 180° from the given sum of interior angles.

3. Importance of Exterior Angle Calculation

Details: Calculating exterior angles is essential in geometry for solving triangle problems, understanding angle relationships, and proving geometric theorems. Exterior angles help determine unknown angles in complex geometric figures.

4. Using the Calculator

Tips: Enter the sum of interior angles in degrees. The value must be greater than 180° to get a positive exterior angle result. For a standard triangle, the sum of interior angles is always 180°.

5. Frequently Asked Questions (FAQ)

Q1: What is the exterior angle theorem?
A: The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles.

Q2: Can exterior angles be negative?
A: No, exterior angles cannot be negative. They are always positive angles between 0° and 180°.

Q3: What is the sum of exterior angles of any polygon?
A: The sum of exterior angles of any convex polygon is always 360°, regardless of the number of sides.

Q4: How do exterior angles relate to interior angles?
A: Exterior and interior angles are supplementary at each vertex of a polygon, meaning they add up to 180°.

Q5: Can this calculator be used for polygons other than triangles?
A: This specific calculator is designed for triangles. For other polygons, different formulas apply to calculate exterior angles.