Triangle: Sum of Remote Interior Angles & Exterior Angle
- A B Cron
An exterior angle of a triangle is the angle formed by extending one of the sides of the triangle past a vertex (the point at which two sides meet). An exterior angle is always supplementary to the interior angle with which it shares a vertex and equal in measure to the sum of the measures of the remote interior angles. Take a look at the figure below, in which δ, the exterior angle, is supplementary to interior angle β: Can you discover this rule? You can move the labels α, β, and γ with your mouse to read.
Make a table on your paper similar to the one above. Copy down the values of each angle α, β, γ, and δ. Use your calculator to find the sum (remember technology tools round off values, so the sum should be an integer.) Can you write the rule?