Question

1. choose the correct answer.

the exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of its ____ interior angles.
equilateral
auxiliary
remote
congruent

1. choose the correct answer.

a corollary to the triangle sum theorem states that the measure of each angle of an equilateral triangle is ____
60°
45°
360°
30°

Explanation:

22.

The Exterior Angle Theorem specifically mentions that an exterior angle of a triangle is equal to the sum of its non - adjacent (remote) interior angles. "Equilateral" refers to a type of triangle, "auxiliary" is not relevant in this theorem context, and "congruent" means equal in measure (not the term used in the theorem).

The Triangle Sum Theorem states that the sum of the interior angles of a triangle is \(180^{\circ}\). For an equilateral triangle, all angles are equal. Let each angle be \(x\). Then \(x + x+x=180^{\circ}\), so \(3x = 180^{\circ}\), and \(x = 60^{\circ}\). \(45^{\circ}\) is for isosceles right - triangles, \(360^{\circ}\) is the sum of angles in a quadrilateral, and \(30^{\circ}\) is not related to the equilateral triangle angle measure from the Triangle Sum Theorem.

Answer:

C. remote

23.