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Chapter 1: Problem 11

What is the difference between complementary and supplementary angles?

Short Answer

Expert verified
Complementary angles add up to 90 degrees. Supplementary angles add up to 180 degrees.

Step by step solution

01

Define Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. For example, if one angle measures 30 degrees, then its complementary angle measures 60 degrees because 30 + 60 = 90.
02

Define Supplementary Angles

Supplementary angles are two angles whose measures add up to 180 degrees. For example, if one angle measures 70 degrees, then its supplementary angle measures 110 degrees because 70 + 110 = 180.
03

Compare Both Types

The key difference between complementary and supplementary angles lies in the sum of their measures. Complementary angles sum up to 90 degrees, while supplementary angles sum up to 180 degrees.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Complementary Angles
Complementary angles are pairs of angles whose measures add up to exactly 90 degrees. Imagine the corner of a piece of paper. The corner forms a right angle, which is 90 degrees. If you were to draw a line starting from the corner and going somewhere inside this angle, you would divide it into two smaller angles. These two new angles are complementary because their measures together still total 90 degrees.
For example:
  • If one angle is 30 degrees, the other must be 60 degrees because 30 + 60 = 90.
  • If one angle is 45 degrees, the other must also be 45 degrees because 45 + 45 = 90.
This relationship is very useful in geometry and trigonometry. Knowing the measure of one complementary angle allows you to easily find the other.
Supplementary Angles
Supplementary angles are pairs of angles whose measures add up to exactly 180 degrees. Picture a straight line. A straight line measures 180 degrees. If you place a point anywhere on that line and draw a line from this point that extends in any direction, you create two angles on either side. These two angles are supplementary.
For example:
  • If one angle is 70 degrees, the other must be 110 degrees because 70 + 110 = 180.
  • If one angle is 100 degrees, the other must be 80 degrees because 100 + 80 = 180.
Supplementary angles help us understand many geometric properties and solve various math problems. It's essential in problems involving parallel lines and transversals.
Geometry Basics
Understanding basic geometry concepts is crucial for mastering more advanced topics. Geometry is the study of shapes, sizes, and properties of figures and spaces. Here are some fundamental ideas:
  • Angles: Angles are formed when two lines meet at a point. Angles are measured in degrees.
  • Types of Angles: Common types of angles include acute (less than 90 degrees), right (exactly 90 degrees), and obtuse (more than 90 degrees, but less than 180 degrees).
  • Lines and shapes: Lines can be parallel, perpendicular, or intersecting. Shapes can be two-dimensional (like squares and circles) or three-dimensional (like cubes and spheres).
Grasping these basics will make it easier for you to tackle more complex geometric problems. For example, knowing the difference between complementary and supplementary angles can help solve for unknown angles in various shapes.

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