{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T07:10:45+00:00","modifiedTime":"2016-03-26T07:10:45+00:00","timestamp":"2022-09-14T17:46:07+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Geometry","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33725"},"slug":"geometry","categoryId":33725}],"title":"Alternate Interior and Exterior Angles —Practice Geometry Questions","strippedTitle":"alternate interior and exterior angles —practice geometry questions","slug":"alternate-interior-and-exterior-angles-practice-geometry-questions","canonicalUrl":"","seo":{"metaDescription":"When two parallel lines are intersected by a third line (called a transversal ), congruent pairs of angles are formed, including alternate interior angles and a","noIndex":0,"noFollow":0},"content":"<p>When two parallel lines are intersected by a third line (called a <i>transversal</i>), congruent pairs of angles are formed, including alternate interior angles and alternate exterior angles. </p>\n<p>The following practice questions ask you to use this information to find a missing angle, and then to apply some algebra to calculate a missing variable.</p>\n<h2 id=\"tab1\" >Practice questions</h2>\n<p>Use the diagram and the given information to solve the problem.</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501499.image0.png\" height=\"184\" alt=\"image0.png\" width=\"300\"/>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">Parallel lines </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501500.image1.png\" height=\"24\" alt=\"image1.png\" width=\"79\"/>\n<p class=\"child-para\">are cut by a transversal. If </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501501.image2.png\" height=\"17\" alt=\"image2.png\" width=\"39\"/>\n<p class=\"child-para\">is represented by</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501502.image3.png\" height=\"40\" alt=\"image3.png\" width=\"125\"/>\n<p class=\"child-para\">is represented by 4<i>x</i> – 45, find the value of <i>x</i><i>.</i></p>\n </li>\n <li><p class=\"first-para\">Parallel lines </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501503.image4.png\" height=\"24\" alt=\"image4.png\" width=\"79\"/>\n<p class=\"child-para\">are cut by a transversal. If </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501504.image5.png\" height=\"17\" alt=\"image5.png\" width=\"103\"/>\n<p class=\"child-para\">are represented by</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501505.image6.png\" height=\"40\" alt=\"image6.png\" width=\"141\"/>\n<p class=\"child-para\">respectively, find the degree measure of </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501506.image7.png\" height=\"17\" alt=\"image7.png\" width=\"25\"/>\n </li>\n</ol>\n<h2 id=\"tab2\" >Answers and explanations</h2>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">20</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501507.image8.png\" height=\"16\" alt=\"image8.png\" width=\"76\"/>\n<p class=\"child-para\">are alternate interior angles. Alternate interior angles are congruent, so set their measures equal to each other and solve for <i>x:</i></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501508.image9.png\" height=\"109\" alt=\"image9.png\" width=\"128\"/>\n </li>\n <li><p class=\"first-para\">140 degrees</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501509.image10.png\" height=\"16\" alt=\"image10.png\" width=\"76\"/>\n<p class=\"child-para\">are alternate exterior angles. Alternate exterior angles are congruent, so set their measures equal to each other and solve for <i>x:</i></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501510.image11.png\" height=\"209\" alt=\"image11.png\" width=\"249\"/>\n<p class=\"child-para\">which means they add up to 180 degrees. Use this info to solve for </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501511.image12.png\" height=\"88\" alt=\"image12.png\" width=\"153\"/>\n </li>\n</ol>","description":"<p>When two parallel lines are intersected by a third line (called a <i>transversal</i>), congruent pairs of angles are formed, including alternate interior angles and alternate exterior angles. </p>\n<p>The following practice questions ask you to use this information to find a missing angle, and then to apply some algebra to calculate a missing variable.</p>\n<h2 id=\"tab1\" >Practice questions</h2>\n<p>Use the diagram and the given information to solve the problem.</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501499.image0.png\" height=\"184\" alt=\"image0.png\" width=\"300\"/>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">Parallel lines </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501500.image1.png\" height=\"24\" alt=\"image1.png\" width=\"79\"/>\n<p class=\"child-para\">are cut by a transversal. If </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501501.image2.png\" height=\"17\" alt=\"image2.png\" width=\"39\"/>\n<p class=\"child-para\">is represented by</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501502.image3.png\" height=\"40\" alt=\"image3.png\" width=\"125\"/>\n<p class=\"child-para\">is represented by 4<i>x</i> – 45, find the value of <i>x</i><i>.</i></p>\n </li>\n <li><p class=\"first-para\">Parallel lines </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501503.image4.png\" height=\"24\" alt=\"image4.png\" width=\"79\"/>\n<p class=\"child-para\">are cut by a transversal. If </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501504.image5.png\" height=\"17\" alt=\"image5.png\" width=\"103\"/>\n<p class=\"child-para\">are represented by</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501505.image6.png\" height=\"40\" alt=\"image6.png\" width=\"141\"/>\n<p class=\"child-para\">respectively, find the degree measure of </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501506.image7.png\" height=\"17\" alt=\"image7.png\" width=\"25\"/>\n </li>\n</ol>\n<h2 id=\"tab2\" >Answers and explanations</h2>\n<ol class=\"level-one\">\n <li><p class=\"first-para\">20</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501507.image8.png\" height=\"16\" alt=\"image8.png\" width=\"76\"/>\n<p class=\"child-para\">are alternate interior angles. Alternate interior angles are congruent, so set their measures equal to each other and solve for <i>x:</i></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501508.image9.png\" height=\"109\" alt=\"image9.png\" width=\"128\"/>\n </li>\n <li><p class=\"first-para\">140 degrees</p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501509.image10.png\" height=\"16\" alt=\"image10.png\" width=\"76\"/>\n<p class=\"child-para\">are alternate exterior angles. Alternate exterior angles are congruent, so set their measures equal to each other and solve for <i>x:</i></p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501510.image11.png\" height=\"209\" alt=\"image11.png\" width=\"249\"/>\n<p class=\"child-para\">which means they add up to 180 degrees. Use this info to solve for </p>\n<img src=\"https://www.dummies.com/wp-content/uploads/501511.image12.png\" height=\"88\" alt=\"image12.png\" width=\"153\"/>\n </li>\n</ol>","blurb":"","authors":[{"authorId":8986,"name":"Allen Ma","slug":"allen-ma","description":" <p><b>Allen Ma </b>and<b> Amber Kuang </b>are math teachers at John F. Kennedy High School in Bellmore, NY. Allen has taught geometry for more than 25 years, has coached the math team, and is a former honors math research coordinator. Amber has taught all levels of math, from algebra to calculus, for 20 years.</p> ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8986"}},{"authorId":8987,"name":"Amber Kuang","slug":"amber-kuang","description":" <p><b>Allen Ma </b>and<b> Amber Kuang </b>are math teachers at John F. Kennedy High School in Bellmore, NY. Allen has taught geometry for more than 25 years, has coached the math team, and is a former honors math research coordinator. Amber has taught all levels of math, from algebra to calculus, for 20 years.</p> ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8987"}}],"primaryCategoryTaxonomy":{"categoryId":33725,"title":"Geometry","slug":"geometry","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33725"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Practice questions","target":"#tab1"},{"label":"Answers and explanations","target":"#tab2"}],"relatedArticles":{"fromBook":[{"articleId":207513,"title":"Geometry: 1001 Practice Problems For Dummies Cheat Sheet","slug":"1001-geometry-practice-problems-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/207513"}},{"articleId":144555,"title":"Circle Basics for Geometry Problems","slug":"circle-basics-for-geometry-problems","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/144555"}},{"articleId":144556,"title":"Coordinate Geometry Formulas","slug":"coordinate-geometry-formulas","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/144556"}},{"articleId":144557,"title":"Geometry Practice Problems with Triangles and Polygons","slug":"geometry-practice-problems-with-triangles-and-polygons","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/144557"}},{"articleId":143448,"title":"Formulas for Geometric Solids Problems","slug":"formulas-for-geometric-solids-problems","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/143448"}}],"fromCategory":[{"articleId":230077,"title":"How to Copy an Angle Using a Compass","slug":"copy-angle-using-compass","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/230077"}},{"articleId":230072,"title":"How to Copy a Line Segment Using a Compass","slug":"copy-line-segment-using-compass","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/230072"}},{"articleId":230069,"title":"How to Find the Right Angle to Two Points","slug":"find-right-angle-two-points","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/230069"}},{"articleId":230066,"title":"Find the Locus of Points Equidistant from Two Points","slug":"find-locus-points-equidistant-two-points","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/230066"}},{"articleId":230063,"title":"How to Solve a Two-Dimensional Locus Problem","slug":"solve-two-dimensional-locus-problem","categoryList":["academics-the-arts","math","geometry"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/230063"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":281917,"slug":"geometry-1001-practice-problems-for-dummies-free-online-practice","isbn":"9781118853269","categoryList":["academics-the-arts","math","geometry"],"amazon":{"default":"https://www.amazon.com/gp/product/1118853261/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1118853261/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1118853261-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1118853261/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1118853261/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/geometry-1001-practice-problems-for-dummies-cover-9781118853269-193x255.jpg","width":193,"height":255},"title":"Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)","testBankPinActivationLink":"","bookOutOfPrint":false,"authorsInfo":"<p><b data-author-id=\"8986\">Allen Ma</b> and <b data-author-id=\"8987\">Amber Kuang</b> are math teachers at John F. 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Alternate Interior and Exterior Angles —Practice Geometry Questions

By: Allen Ma and Amber Kuang and

Updated: 03-26-2016

From The Book: Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)

Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)

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When two parallel lines are intersected by a third line (called a transversal), congruent pairs of angles are formed, including alternate interior angles and alternate exterior angles.

The following practice questions ask you to use this information to find a missing angle, and then to apply some algebra to calculate a missing variable.

Practice questions

Use the diagram and the given information to solve the problem.

Parallel lines

are cut by a transversal. If

is represented by

is represented by 4x – 45, find the value of x.
Parallel lines

are cut by a transversal. If

are represented by

respectively, find the degree measure of

Answers and explanations

20

are alternate interior angles. Alternate interior angles are congruent, so set their measures equal to each other and solve for x:
140 degrees

are alternate exterior angles. Alternate exterior angles are congruent, so set their measures equal to each other and solve for x:

which means they add up to 180 degrees. Use this info to solve for

About This Article

This article is from the book:

Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice) ,

About the book authors:

Allen Ma and Amber Kuang are math teachers at John F. Kennedy High School in Bellmore, New York. Allen, who has taught geometry for 20 years, is the math team coach and a former honors math research coordinator. Amber has taught all levels of mathematics, from algebra to calculus, for the past 14 years.

This article can be found in the category:

Geometry ,