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Chapter 8: Problem 3

Write the measure of the complement and supplement of \(24^{\circ} .\)

Short Answer

Expert verified
The complement of 24 degrees is 66 degrees, and the supplement of 24 degrees is 156 degrees.

Step by step solution

01

Understanding Complements

The complement of an angle is what, when added to the angle, totals 90 degrees. To find the complement of 24 degrees, subtract 24 from 90.
02

Calculating the Complement

Perform the subtraction: 90 - 24 = 66 Therefore, the complement of 24 degrees is 66 degrees.
03

Understanding Supplements

The supplement of an angle is what, when added to the angle, totals 180 degrees. To find the supplement of 24 degrees, subtract 24 from 180.
04

Calculating the Supplement

Perform the subtraction: 180 - 24 = 156 Therefore, the supplement of 24 degrees is 156 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 90 degrees. Imagine you have an angle; if you add another angle to it and their total measure is 90 degrees, these two angles are complementary.

For example: If you have an angle that measures 24 degrees, its complement is found by subtracting the angle from 90 degrees. So, find: \( 90^{\tiny{\text{掳}}} - 24^{\tiny{\text{掳}}} = 66^{\tiny{\text{掳}}} \). The complement of 24 degrees is 66 degrees.

Learn to identify complementary angles in geometry problems. This concept aids in solving more complex angle relationships later on.
supplementary angles
Supplementary angles are pairs of angles whose measures add up to 180 degrees. If you add two angles together and their sum is 180 degrees, these angles are referred to as supplementary angles.

For example: To find the supplement of a 24-degree angle, subtract 24 degrees from 180 degrees: \( 180^{\tiny{\text{掳}}} - 24^{\tiny{\text{掳}}} = 156^{\tiny{\text{掳}}} \). Thus, the supplement of 24 degrees is 156 degrees.

This concept is incredibly useful, especially when dealing with linear pairs of angles or finding unknown angles in various geometric figures.
basic angle calculations
Basic angle calculations involve simple arithmetic to find missing angles based on certain rules like complementary and supplementary angles.

Key points to remember:
  • Complementary angles add up to 90 degrees.
  • Supplementary angles add up to 180 degrees.
  • Use subtraction to find an unknown angle from a given angle.
For example, given a 24-degree angle:

鈥� Complement: \( 90^{\tiny{\text{掳}}} - 24^{\tiny{\text{掳}}} = 66^{\tiny{\text{掳}}} \)
鈥� Supplement: \( 180^{\tiny{\text{掳}}} - 24^{\tiny{\text{掳}}} = 156^{\tiny{\text{掳}}} \)

Practicing these calculations can help you quickly determine missing angles in various geometric problems.

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Most popular questions from this chapter

Identify the units that apply to length. Circle all that apply. a. Yard \(\quad\) b. Ounce \(\quad\) c. Fluid ounce \(\quad\) d. Meter \(\quad\) e. Quart \(\quad\) f. Gram \(\quad\) g. Pound \(\quad\) h. Liter \(\quad\) i. Mile \(\quad\) j. Inch

Define the key terms. a. Rectangular solid b. Cube c. Right circular cylinder d. Right circular cone e. Sphere

Convert the units of area by using multiple factors of the given unit ratio. $$720 \text { in }^{2}=\text{______}\mathrm{ft}^{2}$$

Use a calculator to approximate the square root to three decimal places. $$\sqrt{3184.75}$$

What angle is its own supplement?
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