大学体验英语听说教程2答案_百度文库
两大类热门资源免费畅读
续费一年阅读会员，立省24元！
评价文档：
大学体验英语听说教程2答案
上传于||暂无简介
大小：76.89KB
登录百度文库，专享文档复制特权，财富值每天免费拿！
你可能喜欢Video: How to Measure the Angles of a Polygon & Find the Sum
Watch this video lesson to learn the one formula that lets you find the measure of angles in any regular polygon. Also learn how you can tell if you are working with a regular polygon or not.
An error occurred trying to load this video.
Try refreshing the page, or contact customer support.
You must create an account to continue watching
Register for a free trial
Are you a student or a teacher?
I am a student
What is your educational goal?
Start Your Free Trial To Continue Watching
As a member, you'll also get unlimited access to over
lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.
It only takes a few minutes to set up and you can cancel at any time.
Already registered?
Coming up next:
Ratios and Proportions: Definition and Examples
You're on a roll. Keep up the good work!
Just checking in. Are you still watching?
Your next lesson will play in
10 seconds
Want to watch this again later?
Log in or sign up to add this lesson to a Custom Course.
Organize and save your favorite lessons with Custom Courses
Custom Courses are courses that you create
lessons. Use them just like other courses to
track progress, access quizzes and exams, and share content.
Organize and share selected lessons with your class. Make planning easier by creating your own custom course.
Add important lessons to your Custom Course, track your progress, and achieve your study goals faster.
Create a new course from any lesson page or your dashboard.
From any lesson page:
Click &Add to& located below the video player and follow the prompts to name your course and save your lesson.
From your dashboard:
Click on the &Custom Courses& tab, then click &Create course&. Next, go to any lesson page and begin
adding lessons.
Edit your Custom Course directly from your dashboard.
Personalize:
Name your Custom Course and add an optional description or learning objective.
Create chapters to group lesson within your course. Remove and reorder chapters and lessons at any time.
Share your Custom Course or assign lessons and chapters.
Teacher Edition:
Share or assign lessons and chapters by clicking the &Teacher& tab on the lesson or chapter page you want to
Students' quiz scores and video views will be trackable in your &Teacher& tab.
Premium Edition:
You can share your Custom Course by copying and pasting the course URL.
members will be able to access the
entire course.
Try it free for 5 days!
Recommended Lessons and Courses for You
Instructor:
Yuanxin (Amy) Yang Alcocer
Amy has a master's degree in secondary education and has taught Math at a public charter high school.
Watch this video lesson to learn the one formula that lets you find the measure of angles in any regular polygon. Also learn how you can tell if you are working with a regular polygon or not.
Regular PolygonsOnly with regular polygons can you find the measurement of its angles. What makes a polygon, or a flat shape with straight lines, regular? A regular polygon is defined as a flat shape whose sides are all equal in length and whose angles are all equal. Visually, I like to think of these shapes as wannabe circles. These shapes so want to be circles that they are stretching their ends out as far as they can. Do you see this too? Do you see how if you drew a circle around them, each of the polygon's corners would touch the circle? This is what makes a polygon a regular polygon. Because only regular polygons have a handy and useful formula for calculating the angles, these types of shapes are what we will be considering in this video lesson. Sum of Interior AnglesThe first angle measurement we will discuss is the sum of the measure of interior angles. Long name, I know. All it means is that we are going to find the total measurement of all the interior angles combined. What are the interior angles, you ask? The interior angles are the angles you see inside the polygon at every corner. So a triangle, for example, has three interior angles because it has three corners. A pentagon has five interior angles because it has five corners. Do you see how it works now? It's a good thing for us that we have a very useful formula we can use to find this sum. Sum of the Measure of Interior Angles = (n - 2)*180 Yes, the formula tells us to subtract 2 from n, which is the total number of sides the polygon has, and then to multiply that by 180. We can check this formula to see if it works out. We know that the angles of a triangle will always add up to 180. So let's try finding the sum of interior angles of a regular triangle. We have three sides, so our n is 3. We plug that in and we get (3 - 2)*180 = 1*180 = 180. A-ha! It works! So, whatever regular polygon you have, to find the sum of the measure of interior angles, all you have to do is plug in your number of sides into the n variable and then evaluate. One Interior AngleNow, what about the measure of just one of the interior angles? What do you think we would need to do to find the measure of just one angle if we already know how to find the sum of their measures and that for a regular polygon all the angles are equal? Yes, we would need to divide our sum by the number of sides we have. And that is what our formula tells us to do. Measure of Interior Angle = (n - 2)*180 / n Let's go back to our triangle. We know that an equilateral triangle, a regular triangle, has all of its angles measuring 60 degrees. So, does this check out with our formula? Let's find out. Our regular is a triangle with 3 sides, so our n equals 3. We plug that in to our equation and we get (3 - 2)*180/3 = 1*180/3 = 180/3 = 60. Look at that! It works, too! Likewise, with the sum of the measure of interior angles, we can use this to find the measure of any interior angle of any regular polygon. All we need to do is to plug in our number of sides into the equation.
Unlock Content
Over 30,000 lessons in all major subjects
Get FREE access for 5 days, just create an account.
No obligation, cancel anytime.
Want to learn more?
Select a subject to preview related courses:
Exterior AnglesThe last measurement I want to show you is that of the exterior angle. What is an exterior angle? The exterior angle is the angle you get when you take a side of your polygon and draw it out beyond the shape. When you do this, your interior angle will be inside the polygon and the exterior angle will be the one right next to the interior angle but outside the polygon and formed by the line you extended. Because you extended the side of your polygon, your interior and exterior angle are supplementary angles, meaning that they add up to 180 degrees. We know that a straight line always measures 180 degrees. So because your interior and exterior angles together make up a straight line, they are supplementary. You know how to find the measure of your interior angle, so your exterior angle is simply 180 - Interior Angle. For the triangle, 180 - 60 = 120. 120 degrees is the measure of the exterior angle. One last thing I want to share with you is actually quite interesting. For any regular polygon, if you add up all the exterior angles, they will always add up to 360 degrees. Going back to our triangle, our exterior angle measures 120 and there are three of them, so 120*3 = 360! Pretty cool, huh? Lesson SummaryWow! We've learned quite a bit here! Let's recap. A regular polygon is a flat shape whose sides are all equal and whose angles are all equal. The formula for finding the sum of the measures of the interior angles is (n - 2)*180. To find the measure of one interior angle, we take that formula and divide by the number of sides n: (n - 2)*180 / n. The exterior angle is supplementary to the interior angle, so to find the exterior angle, we simply subtract the interior angle from 180: 180 - interior angle. If we add up all of our exterior angles, we will get 360 degrees.
To unlock this lesson you must be
Register for a free trial
Are you a student or a teacher?
I am a student
What is your educational goal?
Unlock Your Education
See for yourself why 10 million people
member and start learning now.
Already a member?
Earning College Credit
Did you know& We have over 49 college
courses that prepare you to earn
credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the
first two years of college and save thousands off your degree. Anyone can earn
credit-by-exam regardless of age or education level.
To learn more, visit our
Transferring credit to the school of your choice
Not sure what college you want to attend yet?
has thousands of articles about every
imaginable degree, area of
and career path that can help you find the school that's right for you.
Research Schools, Degrees & Careers
Get the unbiased info you need to find the right school.
Browse Articles By Category
Browse an area of study or degree level.
Recommended Articles
Click "next lesson" whenever you finish a lesson and quiz. Got It
You now have full access to our lessons and courses. Watch the lesson now or keep exploring. Got It
You're 25% of the way through this course! Keep going at this rate,and you'll be done before you know it.
The first step is always the hardest! Congrats on finishing your first lesson.
Way to go! If you watch at least 30 minutes of lessons each day you'll master your goals before you know it.
Congratulations on earning a badge for watching 10 videos but you've only scratched the surface. Keep it up!
You've just watched 20 videos and earned a badge for your accomplishment!
You've just earned a badge for watching 50 different lessons. Keep it up, you're making great progress!
You just watched your 100th video lesson. You have earned a badge for this achievement!
Congratulations! You just finished watching your 200th lesson and earned a badge!
Congratulations! You just finished watching your 300th lesson and earned a badge!
You are a superstar! You have earned the prestigious 500 video lessons watched badge.
Incredible. You have just entered the exclusive club and earned the 1000 videos watched badge.
You have earned a badge for watching 20 minutes of lessons.
You have earned a badge for watching 50 minutes of lessons.
You have earned a badge for watching 100 minutes of lessons.
You have earned a badge for watching 250 minutes of lessons.
You have earned a badge for watching 500 minutes of lessons.
You have earned a badge for watching 1000 minutes of lessons.U7听力原文与答案_图文_百度文库
两大类热门资源免费畅读
续费一年阅读会员，立省24元！
U7听力原文与答案
上传于||文档简介
&&施​心​远​主​编​ ​听​力​教​程 ​第​二​版​ ​听​力​原​文​与​答​案
阅读已结束，如果下载本文需要使用1下载券
想免费下载本文？
下载文档到电脑，查找使用更方便
还剩15页未读，继续阅读
你可能喜欢