If the sides of a triangle are extended, what is the sum of the three exterior angles (one at each vertex)?

Introduction / Context:Each exterior angle of a triangle and its adjacent interior angle form a linear pair summing to 180°. Using the fact that the sum of interior angles is 180°, we can deduce the total of all three exteriors.

Given / Assumptions:

• One exterior angle is taken at each vertex (the non-overlapping exterior).

Concept / Approach:Let interior angles be A, B, C with A + B + C = 180°. The corresponding exteriors are 180° − A, 180° − B, 180° − C.

Step-by-Step Solution:Sum of exteriors = (180° − A) + (180° − B) + (180° − C) = 540° − (A + B + C) = 540° − 180° = 360°.

Verification / Alternative check:Draw any acute, right, or obtuse triangle and measure: the three exteriors still sum to a full angle around a point, 360°.

Why Other Options Are Wrong:180°, 90°, 270° misapply the interior-angle sum or count overlapping angles.

Common Pitfalls:Accidentally summing both exterior angles at a vertex; the standard statement uses one exterior at each vertex.

Final Answer:360°