Question

decide if this biconditional statement is true or false. two angles add up to 90° if and only if they are complementary. true false

Explanation:

Step1: Recall the definition of complementary angles

By definition, two angles are complementary if and only if their sum is \(90^{\circ}\).

Step2: Analyze the biconditional statement

The given biconditional statement “Two angles add up to \(90^{\circ}\) if and only if they are complementary” directly aligns with the definition. The “if and only if” part means that both the forward (if two angles are complementary, then they add up to \(90^{\circ}\)) and backward (if two angles add up to \(90^{\circ}\), then they are complementary) implications hold. Since the definition validates both implications, the biconditional statement is true.

Answer:

True