/*! 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 46 Use the five-step problem-solvin... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 46

Use the five-step problem-solving strategy to find the measure of the angle described. The angle's measure is \(78^{\circ}\) less than that of its complement.

Short Answer

Expert verified
The measure of the angle is \(6^{\circ}\)

Step by step solution

01

- Decode the problem and set up an equation

The first step is to understand the problem and set up an equation. We know that in complementary angles, the two angles add up to \(90^{\circ}\). For instance, one angle is \(x\) and its complement will be \(90^{\circ} - x\). According to the problem, the angle is \(78^{\circ}\) less than its complement. So, we can represent it as \(x = 90^{\circ} - x - 78^{\circ}\).
02

- Solve the equation for \(x\)

Now, the equation \(x = 90^{\circ} - x - 78^{\circ}\) should be solved for \(x\). First, combine like terms on the right side of the equation, making it \(x = 12^{\circ} - x\). Then, add \(x\) on both sides to get \(2x = 12^{\circ}\). Lastly, divide both sides by 2 to solve for \(x\). The result is \(x = 6^{\circ}\).
03

- Verify the solution

After finding \(x = 6^{\circ}\), you must verify this solution. The complement of \(6^{\circ}\) is \(90^{\circ} - 6^{\circ} = 84^{\circ}\), which should be \(78^{\circ}\) more than \(x\). Since it is indeed larger than \(6^{\circ}\) by \(78^{\circ}\), \(x = 6^{\circ}\) is confirmed to be the correct solution.

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!

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

Let \(x\) represent the number. Use the given conditions to write an equation. Solve the equation and find the number. Eight subtracted from six times a number is \(298 .\) Find the number.

In your own words, describe a step-by-step approach for solving algebraic word problems.

An automobile repair shop charged a customer 448 dollars listing 63 dollars for parts and the remainder for labor. If the cost of labor is 35 dollars per hour, how many hours of labor did it take to repair the car?

A car can be rented from Basic Rental for 60 dollars per week plus 50 cents for each mile driven. How many miles can you travel if you can spend at most 600 dollars for the week?c

The bar graph shows that average rent and mortgage payments in the United States have increased since \(1975,\) even after taking inflation into account. Exercises \(31-32\) are based on the information displayed by the graph. (GRAPH CANNOT COPY) In \(2008,\) mortgage payments averaged 1514 dollars per month. For the period shown, monthly mortgage payments increased by approximately 20 dollars per year. If this trend continues, how many years after 2008 will mortgage payments average 1714 dollars ? In which year will this occur?
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

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.