The exterior angles of a triangle and the sum of exterior angles
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Welcome to our exploration of exterior angles in triangles. An exterior angle is formed by extending one side of a triangle beyond a vertex. Each exterior angle is supplementary to its adjacent interior angle, meaning they add up to 180 degrees. Remarkably, the sum of all exterior angles of any triangle is always 360 degrees.
Let's examine the key properties of exterior angles. First, an interior angle and its adjacent exterior angle are supplementary - they add up to 180 degrees. Second, any exterior angle of a triangle equals the sum of the two non-adjacent interior angles. These properties make exterior angles very useful in geometric proofs.
To summarize what we've learned about exterior angles: They are formed by extending the sides of a triangle. Each exterior angle is supplementary to its adjacent interior angle. The sum of all exterior angles is always 360 degrees. These properties make exterior angles valuable tools in geometric proofs and problem solving.
Let's examine the key properties of exterior angles. First, an interior angle and its adjacent exterior angle are supplementary - they add up to 180 degrees. Second, any exterior angle of a triangle equals the sum of the two non-adjacent interior angles. These properties make exterior angles very useful in geometric proofs.
Now let's prove that the sum of exterior angles equals 360 degrees. Each exterior angle is supplementary to its interior angle. Since the sum of interior angles in a triangle is 180 degrees, and we have three pairs of supplementary angles, the total of all angles is 540 degrees. Subtracting the 180 degrees from interior angles gives us 360 degrees for the exterior angles.
Let's work through a practical example. Given a triangle with exterior angles of 120, 130, and 110 degrees, we can verify that their sum equals 360 degrees. We can also find the interior angles by subtracting each exterior angle from 180 degrees, giving us 60, 50, and 70 degrees, which correctly sum to 180 degrees.
To summarize our exploration of exterior angles: They are formed by extending the sides of a triangle beyond each vertex. Each exterior angle is supplementary to its adjacent interior angle. Most importantly, the sum of all exterior angles is always 360 degrees, regardless of the triangle's shape. This fundamental property makes exterior angles valuable tools in geometric proofs and problem solving.