Question

which biconditional statement below is true?
angles are congruent if and only if they are vertical angles.
points are collinear if and only if they are coplanar.
angles are supplementary if and only if their sum is 180 degrees.
angles are complementary if and only if each of them are both 90 degrees.

Explanation:

Step1: Analyze each option

• Option 1: Angles are complementary if and only if each of them are both 90 degrees. Complementary angles are two angles whose sum is 90 degrees, not each being 90 degrees. So this is wrong.
• Option 2: Angles are supplementary if and only if their sum is 180 degrees. By the definition of supplementary angles, this is correct.
• Option 3: Points are collinear if and only if they are coplanar. Collinear points lie on the same straight line. Coplanar points lie on the same plane. Collinear points are coplanar but coplanar points are not necessarily collinear. So this is wrong.
• Option 4: Angles are congruent if and only if they are vertical angles. Congruent angles have the same measure. Vertical angles are congruent but there are many non - vertical congruent angles. So this is wrong.

Answer:

Angles are supplementary if and only if their sum is 180 degrees.