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Exterior Angle Formula:
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The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. This fundamental geometric principle helps in solving various triangle-related problems.
The calculator uses the exterior angle formula:
Where:
Explanation: The exterior angle is formed by extending one side of the triangle and is supplementary to the adjacent interior angle.
Details: Calculating exterior angles is essential in geometry for solving triangle problems, proving theorems, and understanding the properties of polygons. It's widely used in architecture, engineering, and various mathematical applications.
Tips: Enter the two non-adjacent interior angles in degrees. Both values must be positive and their sum must be less than 180 degrees to form a valid triangle.
Q1: What is an exterior angle of a triangle?
A: An exterior angle is formed when one side of a triangle is extended. It lies outside the triangle and is adjacent to one of the interior angles.
Q2: Why does the exterior angle equal the sum of two interior angles?
A: This is a fundamental property of triangles proven by the exterior angle theorem, which is derived from the angle sum property of triangles.
Q3: Can the exterior angle be greater than 180 degrees?
A: No, in a triangle, the exterior angle is always less than 180 degrees because the sum of two interior angles is always less than 180 degrees.
Q4: How is this different from the interior angle sum?
A: The interior angle sum is always 180 degrees, while the exterior angle theorem deals with the relationship between an exterior angle and two non-adjacent interior angles.
Q5: Does this work for all types of triangles?
A: Yes, the exterior angle theorem applies to all triangles - equilateral, isosceles, and scalene triangles.