Exterior Angle Theorem Calculator
Exterior angle = Sum of remote interior angles
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Exterior Angle Theorem
An exterior angle of a triangle equals the sum of the two non-adjacent interior angles.
Exterior = Remote₁ + Remote₂
Triangle with Exterior Angle
Understanding the Exterior Angle Theorem
The Exterior Angle Theorem states that an exterior angle of a triangle is equal to the sum of the two non-adjacent (remote) interior angles. This is a powerful theorem for solving triangle problems.
The Theorem
For a triangle with angles A, B, and C:
- Exterior angle at A = B + C
- Exterior angle at B = A + C
- Exterior angle at C = A + B
Why It Works
Since interior + exterior = 180° (linear pair) and A + B + C = 180° (angle sum):
Exterior at C = 180° - C
Since A + B + C = 180°, we have C = 180° - A - B
Therefore: Exterior at C = 180° - (180° - A - B) = A + B ✓
Related Theorem: Exterior Angle Inequality
The exterior angle is greater than either remote interior angle individually:
Exterior at C > A and Exterior at C > B
This follows because A + B > A and A + B > B (assuming positive angles)
Frequently Asked Questions
What is an exterior angle?
An exterior angle is formed by one side of a triangle and the extension of an adjacent side. It forms a linear pair with the interior angle at that vertex.
What are remote interior angles?
Remote interior angles are the two angles of the triangle that are not adjacent to the exterior angle. They are "across" from the exterior angle.
Can the exterior angle equal 180°?
No. If the exterior angle were 180°, the interior angle would be 0°, which isn't possible in a valid triangle. Exterior angles range from greater than 0° to less than 180°.
What is the sum of all exterior angles?
The sum of the three exterior angles of any triangle (one at each vertex) is always 360°.
How is this related to the Triangle Inequality?
The Exterior Angle Inequality (exterior > each remote interior) is related to the Triangle Inequality, as both express fundamental constraints on triangle geometry.