Question

1. the exterior angle of a triangle is equal to the sum of which of the triangles other angles?

the three interior angles

both the adjacent and non - adjacent interior angles

the adjacent interior angle

the two non - adjacent (remote) interior angles

Explanation:

According to the exterior - angle theorem of a triangle, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent (remote) interior angles.

Let the triangle have interior angles \(A\), \(B\), and \(C\), and an exterior angle \(D\) adjacent to angle \(C\). By the angle - sum property of a triangle (\(A + B+C=180^{\circ}\)) and the linear - pair property (\(C + D=180^{\circ}\)), we can substitute \(C = 180^{\circ}-(A + B)\) into \(C + D=180^{\circ}\). Then \(180^{\circ}-(A + B)+D = 180^{\circ}\), which simplifies to \(D=A + B\) (where \(A\) and \(B\) are the non - adjacent interior angles to the exterior angle \(D\)).

The sum of the three interior angles of a triangle is \(180^{\circ}\), and an exterior angle and its adjacent interior angle form a linear pair (\(180^{\circ}\)), so the other options are incorrect.

Answer:

The two non - adjacent (remote) interior angles.