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Exterior Angle Theorem:
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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 theorem helps in understanding triangle geometry and solving various geometric problems.
The calculator uses the Exterior Angle Theorem:
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Explanation: The theorem demonstrates that the exterior angle is always equal to the sum of the two opposite interior angles in any triangle.
Details: Understanding exterior angles is crucial for solving geometric problems, proving triangle congruency, and analyzing polygon properties. It's fundamental in trigonometry and architectural design.
Tips: Enter two non-adjacent interior angles in degrees. Values must be positive and their sum must be less than 180° (since the third angle must complete the triangle).
Q1: Does this theorem apply to all triangles?
A: Yes, the exterior angle theorem holds true for all triangles, regardless of their type (scalene, isosceles, or equilateral).
Q2: What's the relationship between exterior and interior angles?
A: The exterior angle is supplementary to the adjacent interior angle, and equal to the sum of the two opposite interior angles.
Q3: Can I use this for polygons with more than 3 sides?
A: While the theorem specifically applies to triangles, similar concepts exist for polygons, where exterior angles sum to 360°.
Q4: Why must the sum of angles be less than 180°?
A: Because the three interior angles of any triangle must sum to exactly 180°, so any two angles must sum to less than 180°.
Q5: How is this used in real-world applications?
A: This theorem is used in navigation, construction, computer graphics, and any field requiring geometric calculations.