/*! 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 5 An angle with a measure between ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 5

An angle with a measure between \(90^{\circ}\) and \(180^{\circ}\) is a(n) __________ angle.

Short Answer

Expert verified
Obtuse angle

Step by step solution

01

Understand the Range of the Angle

Recognize that the given angle is within the range of more than 90 degrees and less than 180 degrees.
02

Identify the Type of Angle

Recall the definition of different types of angles. An angle that is more than 90 degrees but less than 180 degrees is called an obtuse angle.
03

Conclusion

Based on the definitions, the angle in question 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.

Obtuse Angle
An angle that measures between 90 degrees and 180 degrees is referred to as an obtuse angle. To visualize it, imagine the angle that a partially opened book forms. The pages create an open space wider than a right angle (which is 90 degrees), but not wide enough to become a straight line (180 degrees). This is what we call an obtuse angle.

An obtuse angle is larger than a right angle but smaller than a straight angle.
  • Right angle: Exactly 90 degrees
  • Obtuse angle: Between 90 degrees and 180 degrees
  • Straight angle: Exactly 180 degrees

It鈥檚 important to understand this distinction because it helps in identifying and working with various angles in geometry and practical applications.
Angle Measurement
Angle measurement is a fundamental part of geometry. It tells us the 'openness' between two lines that meet at a point called the vertex. The standard unit of measuring angles is degrees, denoted by the symbol \(^{\circ}\).

Here are some common types of angles based on their measurement:
  • Acute angle: Less than 90 degrees
  • Right angle: Exactly 90 degrees
  • Obtuse angle: Between 90 degrees and 180 degrees
  • Straight angle: Exactly 180 degrees
  • Reflex angle: More than 180 degrees but less than 360 degrees

To measure an angle, we often use a protractor, a semi-circular tool marked in degrees from 0 to 180. By aligning it with the angle's vertex and base, we can see how many degrees separate the two arms of the angle.
Geometry Basics
Geometry is the branch of mathematics that deals with shapes, sizes, and properties of figures. Understanding angles is a key part of this subject. Let鈥檚 break down some basic concepts:
  • Point: A location in space without any size or dimension
  • Line: A straight one-dimensional figure that extends infinitely in both directions
  • Line segment: A part of a line with two endpoints
  • Angle: Formed by two rays (called the sides of the angle) sharing a common endpoint (called the vertex)

In geometry, angles are crucial in defining shapes and understanding their properties. For example, different types of triangles (such as acute, obtuse, and right) are classified based on their angles.

Geometry helps in various real-life applications, including engineering, architecture, and even art. Thus, understanding the basics of geometry can be very practical and useful.

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

Find the degree measure of the smallest positive angle that is coterminal with each angle. $$ 540^{\circ} $$

Find \(f^{-1}(x),\) if \(f(x)=5 x-9\).

Robin Hood plans to use a 30-ft ladder to reach the castle window of Maid Marian. Little John, who made the ladder, advised Robin that the angle of elevation of the ladder must be between \(55^{\circ}\) and \(70^{\circ}\) for safety. What are the minimum and maximum heights that can safely be reached by the top of the ladder when it is placed against the \(50-\mathrm{ft}\) castle wall? Round to the nearest tenth.

Convert each radian measure to degree measure. $$ \frac{3 \pi}{4} $$

Convert each degree measure to radian measure, Give exact answers (in terms of \(\pi\) ). $$ 225^{\circ} $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

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.