/*! 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 48 State whether each angle given i... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 48

State whether each angle given in Exercises \(43-51\) is straight, right, acute, or obtuse. The supplement of an angle measuring \(42^{\circ} .\)

Short Answer

Expert verified
The supplement of an angle measuring 42掳 is 138掳, which is an obtuse angle.

Step by step solution

01

Understand the problem

Given an angle that measures 42 degrees, we need to find its supplement and then classify that supplementary angle as straight, right, acute, or obtuse.
02

Recall the definition of supplementary angles

Two angles are supplementary if the sum of their measures is 180 degrees.
03

Calculate the supplementary angle

Subtract the given angle from 180 degrees: 180掳 - 42掳 = 138掳.
04

Classify the supplementary angle

An angle measuring 138 degrees is greater than 90 degrees and less than 180 degrees. Therefore, it is an obtuse angle.

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.

Types of Angles
When we talk about angles in geometry, there are several types that we need to understand.
  • Acute Angles: These angles measure less than 90 degrees. Examples include 30掳, 45掳, and 60掳.
  • Right Angles: These are exactly 90 degrees. Imagine the corner of a square or the letter 'L'.
  • Obtuse Angles: These measure between 90 and 180 degrees. An example would be 120掳 or 150掳.
  • Straight Angles: These are exactly 180 degrees. They look like a straight line.

Each type of angle has unique properties that help in understanding different geometric concepts and problems. Knowing these types helps in both solving problems and grasping broader concepts in geometry.
Angle Measurement
Angles are measured using degrees (掳). A degree is a unit of measurement that describes the rotation from one direction to another.
  • A full circle is 360 degrees.
  • A straight line, which is a straight angle, is 180 degrees.
  • A right angle is one quarter of a full circle, so it's 90 degrees.

To measure angles, we often use a tool called a protractor. When solving problems involving angles, it's crucial to know how to measure and identify the different angles. In the given problem, we understand that a supplementary angle plus the original angle should total 180 degrees. This helps us find unknown angles using simple subtraction.
Geometry Problem-Solving
Solving geometry problems often involves multiple steps and a solid understanding of various concepts.
  • Identify Known and Unknown Information: Start by identifying what you already know and what you need to find out.
  • Use Definitions and Properties: Use the definitions and properties of geometric figures and angles to set up your equations or solutions. For supplementary angles, remember that their measures add up to 180 degrees.
  • Perform Calculations: Use basic arithmetic to find the missing values. For example, subtract the given angle from 180掳 to find its supplement.
  • Classify the Result: Once you've found the supplementary angle, classify it using the types of angles discussed earlier. This will often involve comparing it against known benchmarks like 90掳 or 180掳.

By breaking problems into smaller steps and using systematic approaches, geometry problem-solving becomes manageable and straightforward.

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

Give the contrapositive of each statement. If I drink orange juice, then I am healthy.

For problems 13-26, explain the reasoning in one or two complete sentences. Can two vertical angles both be acute?

In Exercises \(52-55, \angle A B P\) and \(\angle P B C\) are adjacent angles. Find the measure of \(\angle A B C\) $$m \angle A B P=49^{\circ} 55^{\prime} \text { and } m \angle P B C=57^{\circ} 15^{\prime}$$

The puzzles in Exercises have all been attributed to Englishman Henry Ernest Dudeney \((1857-1930),\) called by some the greatest puzzle writer of all time. Consider the following eight "postulates." a. Smith, Jones, and Rodriquez are the engineer, brakeman, and fireman on a train, not necessarily in that order. b. Riding on the train are three passengers with the same last names as the crewmembers, identified as passenger Smith, passenger Jones, and passenger Rodriquez in the following statements. c. The brakeman lives in Denver. d. Passenger Rodriquez lives in San Francisco. e. Passenger Jones long ago forgot all the algebra that he learned in high school. f. The passenger with the same name as the brakeman lives in New York. g. The brakeman and one of the passengers, a professor of mathematical physics, attend the same health club. h. Smith beat the fireman in a game of tennis at a court near their homes. Can you discover a theorem that tells the name of the engineer? The brakeman? The fireman? Write the theorems in complete sentences.

The puzzles are classic examples and a certain amount of deductive reasoning is required to solve them. Some of these puzzles are quite challenging, so don't be discouraged if you have trouble finding the solution immediately. Ideally they will make you think a bit and, along the way, provide a bit of entertainment. A museum fired an archaeologist who claimed she found a coin dated 300 B.C. Why?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure 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.