Question

question 3 of 10
which is a true statement about an exterior angle of a triangle?
a. it is formed by two segments that are not sides of the triangle.
b. it is formed by two segments that are sides of the triangle.
c. it forms a linear pair with one of the interior angles of the triangle.
d. it is complementary to one of the interior angles of the triangle.

Explanation:

An exterior angle of a triangle is formed by one side of the triangle and the extension of an adjacent side. A linear pair of angles is formed when two adjacent angles form a straight line (sum to \(180^{\circ}\)). An exterior angle and its adjacent interior angle form a linear pair.

• Option A: An exterior angle is formed by a side of the triangle and an extension of an adjacent side (so one segment is a side of the triangle), so this option is incorrect.
• Option B: An exterior angle is formed by a side of the triangle and an extension of an adjacent side (not two sides of the triangle), so this option is incorrect.
• Option C: An exterior angle and its adjacent interior angle form a linear pair (sum to \(180^{\circ}\)), so this option is correct.
• Option D: Complementary angles sum to \(90^{\circ}\). An exterior angle and its adjacent interior angle sum to \(180^{\circ}\) (supplementary, not complementary), so this option is incorrect.

Answer:

C. It forms a linear pair with one of the interior angles of the triangle.