Question

the measures of two angles add to 90° if and only if the angles are complementary. if the measures of two angles do not add to 90°, then the angles are not complementary. if two angles are complementary, then the measures of their angles add to 90.

Explanation:

Step1: Recall contrapositive definition

The contrapositive of a statement "if p then q" is "if not q then not p".

Step2: Analyze first statement

The original statement is "The measures of two angles add to 90° if and only if the angles are complementary". This is equivalent to two - conditional statements: "If the angles are complementary, then the measures of two angles add to 90°" (p→q) and "If the measures of two angles add to 90°, then the angles are complementary" (q→p).

Step3: Find contrapositive of first conditional

For "If the angles are complementary, then the measures of two angles add to 90° (p→q), the contrapositive is "If the measures of two angles do not add to 90°, then the angles are not complementary" (¬q→¬p).

Step4: Find contrapositive of second conditional

For "If the measures of two angles add to 90°, then the angles are complementary" (q→p), the contrapositive is "If the angles are not complementary, then the measures of two angles do not add to 90°".

The second statement "If the measures of two angles do not add to 90°, then the angles are not complementary" is the contrapositive of "If two angles are complementary, then the measures of their angles add to 90°". The third statement "If two angles are complementary, then the measures of their angles add to 90°" is the original conditional part of the biconditional statement.

Answer:

The second statement is the contrapositive of the third statement.