Exterior Angle of Triangle Calculator
The Exterior Angle of Triangle Calculator demonstrates one of geometry’s most useful rules: the Exterior Angle Theorem. This rule states that the exterior angle of a triangle is equal to the sum of the two opposite interior angles. This tool lets you solve for either the exterior angle or a missing interior angle instantly.
Features
Theorem Applied: Automatically applies $d = A + B$.
Dual Functionality: Find the Exterior Angle given two interiors, or find an Interior Angle given the exterior and one interior.
Visual Aid: Defines clearly what ‘Exterior’ means with a diagram extending the triangle’s side.
Logic Display: Shows the simple addition or subtraction used.
How to Use This Calculator
Select Goal: Choose if you are finding the ‘Exterior Angle’ or a ‘Interior Angle’.
Input: Provide the two known angles.
Solve: Click Calculate to find the unknown.
Visualize: The canvas draws the triangle and the extended exterior angle arc.
Formulas
The calculator uses the following mathematical principles:
Exterior Angle Theorem: $$ \text{Exterior Angle} = \text{Interior A} + \text{Interior B} $$
Linear Pair: $$ \text{Exterior Angle} + \text{Adjacent Interior} = 180^{\circ} $$
Finding Interior: $$ \text{Interior A} = \text{Exterior} – \text{Interior B} $$
Practical Applications
Architecture: Designing roof overhangs and angular extensions.
Surveying: Calculating deflection angles for road or path turns.
Naval Navigation: Determining course changes relative to a baseline.
Tips for Success
Definition: An exterior angle is formed by extending one side of the triangle.
Limit: An exterior angle must be greater than either remote interior angle (but less than 180 generally for convex polygons).
Check: The exterior angle plus the adjacent interior angle must always equal 180°.
Frequently Asked Questions (FAQ)
What is a remote interior angle?
It refers to the two angles inside the triangle that are NOT touching the exterior angle.
Does this work for all triangles?
Yes, the Exterior Angle Theorem is true for all plane triangles (acute, obtuse, right).
Final Words
Master the geometry of turns and extensions with the Exterior Angle of Triangle Calculator. It simplifies the relationships between inside and outside angles into a single, easy-to-use tool.
