Question

1. why is $mangle4 + mangle5 + mangle6 = 360^{circ}$?

addition property
subtraction property
triangle sum theorem
exterior angle theorem

Explanation:

• The Addition Property and Subtraction Property are basic arithmetic properties and not related to the sum of angles being \(360^{\circ}\).
• The Triangle Sum Theorem states that the sum of the interior angles of a triangle is \(180^{\circ}\), which is not relevant here.
• The Exterior Angle Theorem (in the context of the sum of exterior angles of a polygon). For any polygon, the sum of its exterior angles is \(360^{\circ}\). When considering the exterior angles \(\angle4\), \(\angle5\), \(\angle6\) (assuming they are the exterior angles of a triangle or a polygon), the sum of exterior angles of a polygon is \(360^{\circ}\) based on the Exterior Angle Theorem concept (where for a triangle, if we extend the sides, the sum of the three exterior angles is \(360^{\circ}\)).

Answer:

Exterior Angle Theorem