Final answer:
The contrapositive of the statement "Two complementary angles have a sum of 90 degrees" is "If two angles do not sum to 90 degrees, then they are not complementary."
Step-by-step explanation:
The question relates to the concept of complementary angles in geometry, a branch of mathematics. The original statement given is "Two complementary angles have a sum of 90 degrees." To write the contrapositive of this statement, we must first identify the hypothesis and conclusion of the original conditional statement:
- If two angles are complementary (hypothesis), then they sum to 90 degrees (conclusion).
The contrapositive of a conditional statement is formed by negating both the hypothesis and conclusion and then reversing them. Hence, the contrapositive of the original statement is:
- If two angles do not sum to 90 degrees (negation of the conclusion), then they are not complementary (negation of the hypothesis).
This is a logical equivalence and maintains the truth value of the original conditional statement, i.e., if the original statement is true, its contrapositive is also true, and vice versa.