Exterior Angles of a Triangle Calculator
Calculate exterior angles using the exterior angle theorem with step-by-step explanations
Triangle Interior Angles
Interior angle at vertex A
Interior angle at vertex B
Interior angle at vertex C
Interior angles sum: 180.0° = 180°
Type: Acute Triangle, Scalene Triangle
Exterior Angles Results
Sum of Exterior Angles
120.0° + 110.0° + 130.0° = 360.0°
Sum of exterior angles always equals 360°
Exterior Angle Theorem Verification
Exterior Angle at A
180° - 60.0° = 120.0°
70.0° + 50.0° = 120.0°
Exterior Angle at B
180° - 70.0° = 110.0°
60.0° + 50.0° = 110.0°
Exterior Angle at C
180° - 50.0° = 130.0°
60.0° + 70.0° = 130.0°
Try These Example Triangles
Key Theorems
Exterior Angle Theorem
An exterior angle of a triangle equals the sum of the two opposite interior angles.
Exterior∠A = ∠B + ∠C
Linear Pair Theorem
An exterior angle and its adjacent interior angle form a linear pair (sum = 180°).
Exterior∠A + Interior∠A = 180°
Sum Property
The sum of all exterior angles (one at each vertex) is always 360°.
Sum of exterior angles = 360°
Triangle Facts
Each triangle has 6 exterior angles (2 at each vertex)
Exterior angles are always greater than either opposite interior angle
In any triangle, the largest exterior angle is opposite the smallest interior angle
The exterior angle theorem is a direct consequence of the angle sum property
Understanding Exterior Angles of Triangles
What is an Exterior Angle?
An exterior angle of a triangle is formed when any side of the triangle is extended. It is the angle between the extended side and the adjacent side of the triangle. Each vertex of a triangle has two exterior angles that are equal to each other.
The Exterior Angle Theorem
The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two opposite interior angles. This is one of the fundamental theorems in triangle geometry.
Calculation Methods
- •Method 1: Subtract interior angle from 180° (linear pair)
- •Method 2: Add the two opposite interior angles (theorem)
Step-by-Step Process
Step 1: Identify Interior Angles
Determine all three interior angles of the triangle. If only two are given, calculate the third using: C = 180° - A - B
Step 2: Apply the Theorem
For each exterior angle, add the two opposite interior angles. For example: Exterior angle at A = B + C
Step 3: Verify Results
Check that the sum of all exterior angles equals 360°, and each exterior angle plus its adjacent interior angle equals 180°
Applications
- ✓Solving unknown angles in triangles
- ✓Proving geometric relationships
- ✓Navigation and surveying calculations
- ✓Architecture and engineering design