Q:

# A(n) _______ angle of a triangle is equal to the sum of the two remote interior angles.-Exterior-Interior-Complementary-Vertical

Accepted Solution

A:
Answer:Option A (Exterior)Step-by-step explanation:To understand this question, it is important to understand the concept of the exterior angle. An exterior angle is an angle which is made by two intersecting lines outside of the shape. Basically, one of the two lines is extended outside the shape. The angle between the extended line and the other line which is not extended is the exterior angle. It is outside the shape. The interior angle is the angle which is made by the same two lines but inside the shape.The sum of the interior angle and the exterior angle is 180 degrees. It is also interesting to note that the sum of the angles in the triangle is 180 degrees.Suppose that the angles in the triangles are A, B, and C, and the associated exterior angle with the angle A is angle D. By the argument, A+B+C=180 degrees and A+D=180 degrees. Since 180 degrees = 180 degrees, therefore A+B+C = A+D. Angle A cancels on both sides and reduces to B+C=D. This proves that the exterior angle of a triangle is equal to the sum of the two remote interior angles!!!