Question

1. why is $\angle1+\angle2+\angle3 = 180^{circ}$?

the exterior angle theorem
the triangle sum theorem
definition of a linear pair
definition of vertical angles

Explanation:

The Triangle Sum Theorem states that the sum of the interior angles of a triangle is \(180^{\circ}\). If \(\angle1\), \(\angle2\), and \(\angle3\) are the interior angles of a triangle, then \(\angle1+\angle2 + \angle3=180^{\circ}\) by this theorem. The Exterior Angle Theorem relates an exterior angle of a triangle to the sum of the two non - adjacent interior angles. The definition of a linear pair is two adjacent angles that are supplementary (sum to \(180^{\circ}\)), but this is for two angles. The definition of vertical angles is about two pairs of opposite angles formed by intersecting lines, with vertical angles being equal.

Answer:

The Triangle Sum Theorem