/*! 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 8 \(A\) \(180^{\circ}\) angle is s... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

\(A\) \(180^{\circ}\) angle is sometimes called a straight angle. Explain why that name makes sense.

Short Answer

Expert verified
A 180° angle is called a straight angle because the two rays extend in opposite directions, forming a straight line.

Step by step solution

01

Understanding Angles

An angle is formed by two rays originating from a common endpoint. The measurement of an angle is the amount of turn between the two rays.
02

Definition of a 180° Angle

A 180° angle is one where the two rays form a straight line when extended in opposite directions from the common endpoint.
03

Visualizing the Angle

Visualize an angle that measures 180°. The rays start together at an endpoint and extend in a straight line in opposite directions.
04

Connecting the Name to the Concept

Since the two rays are in a straight line when at 180°, it makes sense to call this a straight angle. The name comes from the appearance of the rays forming a continuous straight line.

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 91Ó°ÊÓ!

Key Concepts

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

180 degree angle
An angle that measures exactly 180 degrees is known as a straight angle. When you think of a straight angle, imagine two rays originating from the same point but extending in perfectly opposite directions. This creates a straight line, hence the name 'straight angle'.
Straight angles are crucial in various fields of math and real-life applications.
They help us understand basic shapes, construct geometric proofs, and even determine parallel lines. Remember, whenever you see two rays forming a straight line, you're looking at a 180° angle.
angle measurement
Angles play a fundamental role in geometry, and their measurement is essential for understanding their properties. An angle is formed by two rays originating from a common endpoint called the vertex. The measure of an angle is the amount of rotation one ray needs to overlap the other.
This measurement is usually done in degrees, where a full rotation is 360°. Thus, half a rotation, or a straight line, measures 180°. In simpler terms, if you spread your arms straight out to your sides, the angle between your arms is 180 degrees.
Modern tools like protractors make it easier to measure angles, allowing us to ensure precision in construction, navigation, and even art.
rays and endpoints
To fully understand angles, it’s important to grasp the concepts of rays and endpoints. A ray is a part of a line that starts at a particular point, known as the endpoint, and extends infinitely in one direction. When we talk about angles, we usually refer to two such rays originating from the same endpoint.
For example, if you're drawing an angle, you start at a point (the vertex) and extend two lines (rays) outward. The position and the direction of these rays determine the measure and type of the angle formed.
Remember, every angle starts with its vertex (endpoint), and without rays, defining and measuring angles would be impossible. This foundation is crucial for any further study in geometry.

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

Draw a polygon that fits the given description, if possible. If it is not possible, say so. a triangle with just one line of symmetry

Draw two angles that each measure more than \(90^{\circ} .\) Explain how you know they measure more than \(90^{\circ}\).

You can produce a sequence of numbers by applying this rule to each term: If the number is even, get the next number by dividing by \(2 .\) If the number is odd, get the next number by multiplying by 3 and adding 1. a. Use this rule to produce a sequence with 1 as the first term. Describe the pattern in the sequence. b. Now use the rule to produce a sequence with 8 as the first term. Keep finding new terms until you see a pattern in the sequence. Describe what happens. c. Use the rule to generate two more sequences. Keep finding new terms until you see a pattern. d. Using your calculator and the rule, generate a sequence with 331 as its first term. Again, keep finding new terms until you see a pattern. e. Describe what you discovered in Parts a-d.

If the given measures could be the measures of two angles of a triangle, give the measure of the third angle. If not, explain why. \(60^{\circ}, 60^{\circ}\)

One mile is about 1.6 kilometers. a. Which is the greater distance, 1 mile or 1 kilometer? b. Los Angeles and New York City are about 2,460 miles apart. How many kilometers apart are they? c. If the speed limit on a road in Canada is 50 kilometers per hour, what is the speed limit in miles per hour? d. In Investigation \(2,\) you learned that lightning is 1 mile away for every 5 seconds you count between the lightning and the following clap of thunder. About how many seconds would it take you to hear the thunder if the lightning were 1 kilometer away?

See all solutions

Recommended explanations on Math Textbooks

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.