What is the relationship between complementary and supplementary angles?

Complementary and supplementary angles have specific relationships based on their sums:

1. **Complementary Angles**:
   - Two angles are complementary if the sum of their measures is \(90^\circ\).
   - Example: If one angle measures \(30^\circ\), the complementary angle must measure \(60^\circ\) because \(30^\circ + 60^\circ = 90^\circ\).

2. **Supplementary Angles**:
   - Two angles are supplementary if the sum of their measures is \(180^\circ\).
   - Example: If one angle measures \(110^\circ\), the supplementary angle must measure \(70^\circ\) because \(110^\circ + 70^\circ = 180^\circ\).

These relationships are fundamental in geometry and are often used to solve problems involving angles in various geometric figures.

Would you like more details or have any other questions? Here are 5 numbered questions you might find useful:

1. How do you find the sum of the interior angles of a polygon?
2. How do you solve for an unknown angle in a right triangle?
3. What are the properties of an isosceles triangle?
4. How do you use the Pythagorean theorem to find the length of a side in a triangle?
5. How do you calculate the area of a circle?

**Tip:** Practice identifying complementary and supplementary angles in different geometric figures to strengthen your understanding of these concepts.

Explore the relationship between complementary and supplementary angles in geometry. Learn how to identify and calculate these angles with examples and explanations. Suitable for students in Grades 6-8.

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