Which statement represents the Triangle Sum Theorem?

Which statement represents the Triangle Sum Theorem?

• A. The exterior angles add to 360 degrees.
• B. All angles are 60 degrees.
• C. The interior angles add to 180 degrees.
• D. The sum is 90 degrees.

Answer: (C)

Inside any triangle drawn on a flat plane, the three interior angles always add up to 180 degrees. This is the Triangle Sum Theorem. A clear way to see it is to label the triangle as A, B, C and draw a line through A that is parallel to BC. Because of parallel lines, the angle at B matches the angle formed by AB with that parallel line, and the angle at C matches the angle formed by AC with that parallel line. The three angles along that straight line add up to 180 degrees, so angle A plus angle B plus angle C equals 180 degrees. That makes the statement about the interior angles summing to 180 degrees the correct description of the theorem. The other ideas don’t hold in general: not all triangles have angles of 60 degrees, the sum is not 90 degrees, and exterior angles summing to 360 degrees describe a different property.

Inside any triangle drawn on a flat plane, the three interior angles always add up to 180 degrees. This is the Triangle Sum Theorem. A clear way to see it is to label the triangle as A, B, C and draw a line through A that is parallel to BC. Because of parallel lines, the angle at B matches the angle formed by AB with that parallel line, and the angle at C matches the angle formed by AC with that parallel line. The three angles along that straight line add up to 180 degrees, so angle A plus angle B plus angle C equals 180 degrees. That makes the statement about the interior angles summing to 180 degrees the correct description of the theorem. The other ideas don’t hold in general: not all triangles have angles of 60 degrees, the sum is not 90 degrees, and exterior angles summing to 360 degrees describe a different property.