Exterior Angle Theorem states that the measure of an exterior angle equals what?

Exterior Angle Theorem states that the measure of an exterior angle equals what?

• A. An exterior angle equals the sum of the two nonadjacent interior angles.
• B. An exterior angle equals the adjacent interior angle.
• C. An exterior angle equals the sum of all interior angles.
• D. An exterior angle equals twice the opposite interior angle.

Answer: (A)

The exterior angle of a triangle equals the sum of the measures of the two interior angles not adjacent to it. This works because the exterior angle forms a linear pair with the adjacent interior angle, so together they add to 180 degrees; and the sum of all three interior angles is also 180 degrees. Therefore, the exterior angle must equal the sum of the other two interior angles—the remote interior angles. For example, if the two nonadjacent interior angles measure 30 and 40 degrees, the exterior angle would be 70 degrees. This aligns with the theorem and shows why the statement is correct. The adjacent interior angle alone isn’t equal to the exterior angle (they’re supplementary), and the exterior angle isn’t the sum of all interior angles or twice any interior angle.

The exterior angle of a triangle equals the sum of the measures of the two interior angles not adjacent to it. This works because the exterior angle forms a linear pair with the adjacent interior angle, so together they add to 180 degrees; and the sum of all three interior angles is also 180 degrees. Therefore, the exterior angle must equal the sum of the other two interior angles—the remote interior angles.

For example, if the two nonadjacent interior angles measure 30 and 40 degrees, the exterior angle would be 70 degrees. This aligns with the theorem and shows why the statement is correct. The adjacent interior angle alone isn’t equal to the exterior angle (they’re supplementary), and the exterior angle isn’t the sum of all interior angles or twice any interior angle.