Question

1. why is $mangle1 + mangle2 + mangle3 + mangle4 + mangle5 + mangle6 = 540^{circ}$? addition property subtraction property triangle sum theorem exterior angle theorem

Explanation:

The sum of the exterior angles of a polygon is calculated using the formula \((n - 2)\times180^{\circ}\), where \(n\) is the number of sides of the polygon. For a pentagon (\(n=5\)), \((5 - 2)\times180^{\circ}= 540^{\circ}\). The Exterior Angle Theorem states that the sum of the exterior angles of a polygon is \(360^{\circ}\) for a convex polygon. But if we consider the angles as described (assuming a pentagon - like structure with 6 angles which might be a mis - count or a special case where adjacent angles are considered), the formula related to the sum of angles in a polygon (a form of the Exterior Angle Theorem application for a 5 - sided figure in terms of angle sum) is used. The Addition and Subtraction Properties are basic arithmetic properties and not relevant for angle sum in polygons. The Triangle Sum Theorem is for the sum of angles in a triangle (\(180^{\circ}\)).

Answer:

Exterior Angle Theorem