Question

27 what is the sum of the exterior angles of any polygon? (1) $90^circ$ (2) $180^circ$ (3) $270^circ$ (4) $360^circ$

Explanation:

Step1: Recall the exterior angle sum theorem

The exterior angle sum theorem for polygons states that the sum of the exterior angles of any convex polygon (one at each vertex) is always \(360^\circ\). This holds true for any polygon, whether it is a triangle, quadrilateral, pentagon, etc.

Step2: Evaluate the options

• Option (1): \(90^\circ\) is not the sum of exterior angles of any polygon.
• Option (2): \(180^\circ\) is the sum of interior angles of a triangle, not exterior angles of any polygon.
• Option (3): \(270^\circ\) is not the sum of exterior angles of any polygon.
• Option (4): \(360^\circ\) matches the exterior angle sum theorem for any polygon.

Answer:

(4) \(360^\circ\)