Question

7
which is a true statement about an exterior angle of a triangle?
a. it forms a linear pair with one of the interior angles of the triangle.
b. it is formed by two segments that are sides of the triangle.
c. it is formed by two segments that are not sides of the triangle.
d. it is complementary to one of the interior angles of the triangle.

Explanation:

To determine the true statement about an exterior angle of a triangle, we analyze each option:

• Option A: An exterior angle of a triangle is formed by extending one side of the triangle. The exterior angle and the adjacent interior angle form a linear pair (they are supplementary and adjacent, forming a straight line). This is a fundamental property of exterior angles of triangles.
• Option B: An exterior angle is not formed by two sides of the triangle. It is formed by one side of the triangle and the extension of another side, so this is false.
• Option C: An exterior angle is formed by one side of the triangle and the extension of another side, so one of the segments is a side of the triangle. Thus, this is false.
• Option D: An exterior angle is supplementary (not complementary) to its adjacent interior angle, and it is equal to the sum of the two non - adjacent interior angles. So this is false.

Answer:

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