Question
Is the following biconditional true? Two angles are complementary if and only if their measures add up to 90 degrees. yes no
Ask by Brewer Turnbull. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The biconditional statement is true.
Solution
**Yes**, the biconditional statement is true.
**Explanation:**
A biconditional statement "P if and only if Q" means that both "P implies Q" and "Q implies P" are true.
- **If two angles are complementary, then their measures add up to 90 degrees.**
This aligns with the definition of complementary angles.
- **If the measures of two angles add up to 90 degrees, then the angles are complementary.**
This also aligns with the definition.
Since both directions hold true, the biconditional statement is indeed true.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
Absolutely, it's true! Two angles are indeed complementary if their measures sum to 90 degrees. This relationship is foundational in geometry and often appears in various proofs and theorems, making it essential for students to grasp. In real-world situations, complementary angles can be observed in design and architecture. For example, the angles of a right triangle (which is always 90 degrees) can showcase complementary angles, playing key roles in constructing buildings, designing furniture, or even creating art.
