/*! 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 23 Classify each angle as acute, ob... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 23

Classify each angle as acute, obtuse, right, or straight. $$110^{\circ}$$

Short Answer

Expert verified
The angle \(110^{ ext{掳}}\) is an obtuse angle.

Step by step solution

01

Understand the Types of Angles

To classify angles, let's first understand the categories:- **Acute Angle:** An angle less than \(90^{ ext{掳}}\).- **Right Angle:** An angle exactly \(90^{ ext{掳}}\).- **Obtuse Angle:** An angle greater than \(90^{ ext{掳}}\) but less than \(180^{ ext{掳}}\).- **Straight Angle:** An angle exactly \(180^{ ext{掳}}\).
02

Identify the Given Angle

In this exercise, the given angle is \(110^{ ext{掳}}\). We need to determine which category this angle falls into based on its measure.
03

Compare the Angle to Definitions

To classify \(110^{ ext{掳}}\), compare it with the angle definitions:- \(110^{ ext{掳}}\) is greater than \(90^{ ext{掳}}\) but less than \(180^{ ext{掳}}\).- Therefore, \(110^{ ext{掳}}\) is an obtuse angle because it meets the criteria for being greater than \(90^{ ext{掳}}\) but less than \(180^{ ext{掳}}\).

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.

Acute Angle
An acute angle is a charming type of angle defined by its measure of being less than 90 degrees. While it may be small, it plays a significant role in various geometric contexts. Think of it as the angle of choice when something needs to be sharp or concise without being overly steep or flat.
  • An acute angle is always less than a right angle.
  • Examples include angles like 30掳, 45掳, and 60掳.
These angles are commonly seen in triangles, particularly in equilateral and right-angled triangles, where they complement other angles. Whenever you hear 'acute,' think sharp and small, just like the word sounds.
Obtuse Angle
An obtuse angle is broader and more expansive, being larger than a right angle. It measures greater than 90 degrees but less than 180 degrees. This gives obtuse angles a more open appearance, often suggesting a relaxed and wide-opening.
  • Obtuse angles are always greater than acute angles.
  • Examples include angles like 110掳, 120掳, and 150掳.
This angle type is less common in regular polygons but incredibly useful in design and aesthetics where a wide spread or embrace is needed. In art and architecture, these angles can create striking and elegant features.
Right Angle
The right angle is iconic with its exact measure of 90 degrees. It is the hallmark of perpendicular intersections, forming perfectly square corners. When anything is at a right angle, it signifies uprightness and stability.
  • Right angles are found in many everyday objects like books, doors, and windows.
  • It is a cornerstone in geometry, often used as a reference to ensure accuracy in constructions.
In mathematics, the right angle marks a point of balance between smaller acute angles and larger obtuse or straight angles. It is as if it stands guard, reminding us of precision and balance in our calculations and designs.
Straight Angle
A straight angle stands apart with its measure of exactly 180 degrees. It is the angle that creates a line, representing a perfect and unchanging direction. Think of a straight angle as the seamless flow from one point to another along a flat line.
  • Straight angles divide a plane into two equal halves.
  • They are the result of aligning two rays in opposite directions.
In daily life, straight angles communicate continuation or progression, and in geometry, they are foundational in understanding parallel lines and transformations. Whenever you look at a flat door or a level horizon, you are witnessing the essence of a straight angle.

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

Name all of the sets of numbers to which each real number belongs. Let \(\mathbf{N}=\) natural numbers, \(\mathbf{W}=\) whole numbers, \(\mathbf{Z}=\) integers, \(\mathbf{Q}=\) rational numbers, and I = irrational numbers. $$4$$

Determine whether each statement is sometimes, always, or never true. An irrational number is a negative integer.

Name all of the sets of numbers to which each real number belongs. Let \(\mathbf{N}=\) natural numbers, \(\mathbf{W}=\) whole numbers, \(\mathbf{Z}=\) integers, \(\mathbf{Q}=\) rational numbers, and I = irrational numbers. $$-\frac{56}{8}$$

LANDSCAPING A sprinkler waters a circular area of the lawn as shown. The formula \(A=3.14 r^{2}\) measures the distance \(r\) the sprinkler shoots water within a circular area \(A .\) How far is the sprinkler shooting water if it waters an area of 572.6 square feet? Round to the nearest tenth. (figure can't copy)

Find the distance between each pair of points. Round to the nearest tenth, if necessary. $$M(0,0), N(-7,-8)$$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.