Exterior Angles Of A Triangle
Calculate the exterior angle of a triangle given two interior angles using the exterior angle theorem. Free online geometry calculator for students and teachers.
About This Calculator
This Exterior Angles of a Triangle Calculator uses the exterior angle theorem to compute the exterior angle of a triangle. Given any two interior angles, the calculator finds the exterior angle at the third vertex, the adjacent interior angle, and the opposite interior angle.
The exterior angle theorem states that the exterior angle of a triangle equals the sum of the two remote (non-adjacent) interior angles. This is a fundamental property of triangles in Euclidean geometry and is widely used in geometry proofs, construction problems, and architectural design. After finding the exterior angle, the third interior angle is also computed because the three interior angles must sum to 180 deg.
The exterior angle theorem is applied in fields such as architecture (roof trusses and structural angles), navigation (bearing calculations), computer graphics (polygon rendering and lighting), and surveying (angle measurements and triangulation). Understanding exterior angles is essential for geometry students preparing for board exams and competitive tests worldwide.
Frequently Asked Questions
What is the exterior angle theorem?
The exterior angle theorem states that the exterior angle of a triangle equals the sum of the two opposite (non-adjacent) interior angles. If you know the two remote interior angles, the exterior angle is simply their sum.
How do you find the exterior angle of a triangle?
To find an exterior angle of a triangle, add the two non-adjacent interior angles. For example, if interior angles A = 50 deg and B = 60 deg, the exterior angle at C = A + B = 110 deg.
What is the relationship between exterior and interior angles?
An exterior angle and its adjacent interior angle are supplementary (they add up to 180 deg). Additionally, the exterior angle equals the sum of the two remote interior angles.
Can an exterior angle be greater than 180 deg?
No, for a triangle, the exterior angle ranges between 0 deg and 180 deg (exclusive). Since interior angles are all between 0 deg and 180 deg, their sum (the exterior angle) cannot reach or exceed 180 deg.
How many exterior angles does a triangle have?
A triangle has 6 exterior angles -- one at each vertex on each side of the triangle. However, the exterior angles on the same side of a vertex are vertically opposite and equal.
What is the sum of exterior angles of a triangle?
The sum of the three exterior angles of any triangle (taking one at each vertex) is always 360 deg. This is true for any convex polygon.