Exterior Angles of a Triangle Calculator With Points

Exterior Angles Calculation:

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

Exterior Angle at A:

Exterior Angle at B:

Exterior Angle at C:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What Are Exterior Angles?

An exterior angle of a triangle is formed by one side of the triangle and the extension of an adjacent side. The sum of the exterior angles of any polygon is always 360 degrees.

2. How Does the Calculator Work?

The calculator uses vector mathematics to determine the angles:

\[ \text{Angle} = \arccos\left(\frac{\vec{v_1} \cdot \vec{v_2}}{|\vec{v_1}| \times |\vec{v_2}|}\right) \]

Where:

\( \vec{v_1}, \vec{v_2} \) — Vectors forming the angle
\( \cdot \) — Dot product operation
\( |\vec{v}| \) — Magnitude of the vector
Exterior angle = 180° - Interior angle

3. Importance of Exterior Angles

Details: Exterior angles are important in geometry, computer graphics, and navigation. They help in understanding polygon properties and solving various geometric problems.

4. Using the Calculator

Tips: Enter the x,y coordinates of three points that form a triangle. The calculator will compute the exterior angles at each vertex.

5. Frequently Asked Questions (FAQ)

Q1: What is the sum of exterior angles of a triangle?
A: The sum is always 360 degrees, regardless of the triangle's shape or size.

Q2: How are exterior angles related to interior angles?
A: Each exterior angle is supplementary to its adjacent interior angle (they add up to 180 degrees).

Q3: Can this calculator handle degenerate triangles?
A: No, the points must form a valid triangle (not colinear).

Q4: What units are used for the coordinates?
A: The units can be any consistent length unit (pixels, meters, etc.) as only the relative positions matter.

Q5: Why calculate from points instead of side lengths?
A: Point coordinates are often more readily available in applications like computer graphics and surveying.