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

Complementary angles are defined as two angles whose sum is \(90^{\circ}\).

Step2: Analyze the biconditional statement

The biconditional statement "Two angles add up to \(90^{\circ}\) if and only if they are complementary" is in line with the definition. If two angles are complementary (\(p\)), then they add up to \(90^{\circ}\) (\(q\)) (\(p\Rightarrow q\)). Also, if two angles add up to \(90^{\circ}\) (\(q\)), then they are complementary (\(p\)) (\(q\Rightarrow p\)). Since both implications hold, the biconditional statement is true.

Answer:

True