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Chapter 8: Problem 34

The measure of an angle is given. Find the measure of the complement. $$5^{\circ}$$

Short Answer

Expert verified
85 degrees

Step by step solution

01

Understand Complementary Angles

Complementary angles are two angles whose sum is equal to 90 degrees.
02

Set Up the Equation

Let the measure of the given angle be 5 degrees. Let the measure of its complement be denoted as \( x \). The equation for complementary angles is: \( 5 + x = 90 \).
03

Solve for the Complement

Subtract the measure of the given angle from 90 degrees to find the complement: \( x = 90 - 5 \).
04

Calculate the Complement

Perform the subtraction: \( 90 - 5 = 85 \). Thus, the complement of a 5-degree angle is 85 degrees.

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Key Concepts

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

angle measurement
Angle measurement is a fundamental concept in basic geometry. Angles are usually measured in degrees, which tell us how 'open' or 'closed' an angle is. The full circle is 360 degrees, a straight line is 180 degrees, and a right angle is 90 degrees.
When dealing with complementary angles, which are two angles whose measures add up to 90 degrees, it is essential to be comfortable with measuring and finding the size of angles. Understanding how to measure angles helps us in various geometry problems and real-life applications.
  • Always make sure your angles and calculations are accurate.
  • Double-check your angle measurements starting from a common reference, like the base line of a protractor.
  • Getting very familiar with standard angle measures (like 30掳, 45掳, 60掳, and 90掳) can make many problems easier.
basic geometry
Basic geometry involves the study of shapes, sizes, and properties of figures. It includes understanding different types of angles and their relationships. Complementary angles are a basic yet crucial concept within geometry, often introduced early in a geometry curriculum.
When working with complementary angles, you're dealing with a pair of angles that together sum to 90 degrees. These angles can appear in various geometric scenarios, such as when two angles form a right angle.
  • Practicing problems involving complementary angles helps solidify the concept.
  • It is helpful to visualize and draw diagrams to see how different geometric figures and angles interact.
  • Knowing definitions and properties of angles and other geometric shapes is key for solving broader geometry problems.
subtraction
Subtraction is a fundamental arithmetic operation that is particularly useful for solving geometry problems involving angles. For complementary angles, we often need to subtract the given angle from 90 degrees to find its complement.
For example, given a 5-degree angle as in the problem, we subtract this from 90 degrees to find its complement: \( x = 90 - 5 \), which equals 85 degrees.
  • Always ensure your subtraction is accurate.
  • Use simple arithmetic checks to ensure the sum of complementary angles equals 90 degrees.
  • Practicing basic subtraction with real-world examples helps improve numerical dexterity and confidence.

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