/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 39 The measure of an angle is given... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 39

The measure of an angle is given. Find the measure of the complement. $$89^{\circ}$$

Short Answer

Expert verified
1掳

Step by step solution

01

Understand the concept of complementary angles

Complementary angles are two angles whose measures add up to 90 degrees. If you have one angle, you can find its complement by subtracting the measure of the given angle from 90 degrees.
02

Set up the equation

Let the measure of the given angle be denoted as \theta. Therefore, the complement of this angle is calculated using the equation: \[ 90^{\circ} - \theta \]
03

Substitute the given angle

Substitute \(\theta = 89^{\circ}\) into the equation from Step 2: \[ 90^{\circ} - 89^{\circ} = 1^{\circ} \]
04

Calculate the result

Perform the subtraction: \[ 1^{\circ} \] Therefore, the measure of the complement of an \(89^{\circ}\) angle is \(1^{\circ}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Understanding Angle Measurement
Angles are a fundamental concept in geometry. They are formed by two rays (or lines) originating from the same point, known as the vertex. The space between these two rays is what we measure as an angle. The most common unit for measuring angles is degrees, denoted by the symbol \( ^{\text{o}} \).

In a full circle, there are 360 degrees. Angles can vary in size:
  • An angle less than 90 degrees is called an acute angle.
  • An angle equal to 90 degrees is called a right angle.
  • An angle between 90 and 180 degrees is known as an obtuse angle.
  • An angle of exactly 180 degrees is a straight angle.
Understanding how to measure angles is vital for solving geometric problems.
Basic Geometry Concept: Complementary Angles
In basic geometry, complementary angles are two angles whose measures add up to 90 degrees. This relationship is crucial when working on various geometry problems. For instance, if you know one angle in a pair of complementary angles, you can easily find the other by using a simple subtraction method.

The key to solving for the complementary angle is: \[\text{{Complementary Angle}} = 90^{\text{o}} - \theta\]

Where \(\theta\) is the measure of the given angle. Complementary angles often appear in real-life scenarios and more complex geometric figures. Recognizing and calculating these can help in finding unknown angles and enhancing understanding of geometric relationships.
Performing Angle Subtraction
Subtraction is a basic arithmetic operation that we often use in geometry to find unknown angle measures. When given one angle, you can find its complement by subtracting it from 90 degrees.

Let's say you have an angle of \( 89^{\text{o}} \). You want to find its complement. The steps are straightforward:
  • Write down the complement equation: \( 90^{\text{o}} - \theta \)
  • Substitute the given angle into the equation: \( 90^{\text{o}} - 89^{\text{o}} \)
  • Perform the subtraction: \( 1^{\text{o}} \)
Therefore, the complement of an \( 89^{\text{o}} \) angle is \( 1^{\text{o}} \).

This method works for any given angle less than 90 degrees. It's a simple but effective way to handle many geometry problems.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Determine the surface area of the object described. Use 3.14 for \(\pi\) when necessary. A rectangular solid with dimensions \(8 \mathrm{m}\) by \(7 \mathrm{m}\) by \(5 \mathrm{m}\)

Can two supplementary angles both be obtuse? Why or why not?

The second hand on a clock sweeps out a complete circle in 1 min. A circle forms a \(360^{\circ}\) arc. Use this information. (IMAGE CAN'T COPY) How many degrees does a second hand on a clock move in 30 sec?

A square tile is \(110 \mathrm{mm}\) in length. If they are placed side by side, how many tiles will it take to cover a length of wall \(1.43 \mathrm{m}\) long?

The second hand on a clock sweeps out a complete circle in 1 min. A circle forms a \(360^{\circ}\) arc. Use this information. (IMAGE CAN'T COPY) How many degrees does a second hand on a clock move in 45 sec?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.