{"id":71968,"date":"2021-02-04T15:17:37","date_gmt":"2021-02-04T09:47:37","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=71968"},"modified":"2021-02-04T15:17:41","modified_gmt":"2021-02-04T09:47:41","slug":"rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/","title":{"rendered":"RD Sharma Chapter 8 Class 9 Maths Exercise 8.1 Solutions"},"content":{"rendered":"\n<p>We will learn about the Lines and Angles in RD Sharma Chapter 8 Class 9 Maths Exercise 8.1 Solutions. The exercise is all about the Types of Angles, Axioms &amp; Theorems, Angle Bisector, Congruent Angles, etc. To make the concepts easy for the students, we have provided the exercise with easy solutions, which helps them score well in the exam. The questions mentioned in the PDF is taken from the CBSE Text Book, RD Sharma, and Previous Years Question Paper of Class 9. From this chapter, students specifically learn about the formulas and techniques for solving the questions related to the Lines and Angles.<\/p>\n<p>Download the RD Sharma Chapter 8 Class 9 Maths Exercise 8.1 Solutions PDF for free attached below for the students from which they can practice for the exam. There are various types of questions related to the Types of Angles, Axioms &amp; Theorems, etc. By practicing regularly, students get expert in using the formulas and techniques provided by our experts to solve the questions efficiently.<\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-9-maths-chapter-8-lines-and-angles\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Click Here<\/strong><\/a> to know about the Introduction of Lines and Angles<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69d7c22c1d44e\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #000000;color:#000000\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-69d7c22c1d44e\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/#download-rd-sharma-chapter-8-class-9-maths-exercise-81-solutions-pdf\" title=\"Download RD Sharma Chapter 8 Class 9 Maths Exercise 8.1 Solutions PDF\">Download RD Sharma Chapter 8 Class 9 Maths Exercise 8.1 Solutions PDF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/#important-definitions-rd-sharma-chapter-8-class-9-maths-exercise-81-solutions\" title=\"Important Definitions RD Sharma Chapter 8 Class 9 Maths Exercise 8.1 Solutions\">Important Definitions RD Sharma Chapter 8 Class 9 Maths Exercise 8.1 Solutions<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/#angles\" title=\"Angles\">Angles<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/#parts-of-angles\" title=\"Parts of Angles\">Parts of Angles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/#classification-of-angles\" title=\"Classification of Angles\">Classification of Angles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/#types-of-angles\" title=\"Types of Angles\">Types of Angles<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/#interior-and-exterior-of-an-angle\" title=\"Interior and Exterior of An Angle\">Interior and Exterior of An Angle<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/#interior-of-an-angle\" title=\"Interior of An Angle\">Interior of An Angle<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/#the-exterior-of-an-angle\" title=\"The exterior of An Angle\">The exterior of An Angle<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/#congruent-angles\" title=\"Congruent Angles\">Congruent Angles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/#the-measure-of-an-angle\" title=\"The Measure of An Angle\">The Measure of An Angle<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/#axioms-and-theorems\" title=\"Axioms and Theorems\">Axioms and Theorems<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/#complementary-angles\" title=\"Complementary Angles\">Complementary Angles<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/#facts-of-complementary-angles\" title=\"Facts of Complementary Angles\">Facts of Complementary Angles<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/#supplementary-angles\" title=\"Supplementary Angles\">Supplementary Angles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/#angle-bisector\" title=\"Angle Bisector\">Angle Bisector<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-chapter-8-class-9-maths-exercise-81-solutions-pdf\"><\/span>Download RD Sharma Chapter 8 Class 9 Maths Exercise 8.1 Solutions PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/Solutions-for-Class-9-Maths-Chapter-8-Lines-and-Angles-Exercise-8.1.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/Solutions-for-Class-9-Maths-Chapter-8-Lines-and-Angles-Exercise-8.1.pdf\">Solutions for Class 9 Maths Chapter 8 Lines and Angles Exercise 8.1<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"important-definitions-rd-sharma-chapter-8-class-9-maths-exercise-81-solutions\"><\/span>Important Definitions RD Sharma Chapter 8 Class 9 Maths Exercise 8.1 Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Look down to the following to know the brief about the definitions and illustrations based on the RD Sharma Chapter 8 Class 9 Maths Exercise 8.1 Solutions Lines and Angles. This includes the topics and subtopics, namely-<\/p>\n<ol>\n<li>Angles<\/li>\n<li>Interior of an angle<\/li>\n<li>The exterior of an angle<\/li>\n<li>Congruent angles<\/li>\n<li>The measure of an angle<\/li>\n<li>Axioms and Theorems<\/li>\n<li>Types of Angles<\/li>\n<\/ol>\n<ul>\n<li>1. Right Angle<\/li>\n<li>2. Acute Angle<\/li>\n<li>3. Obtuse Angle<\/li>\n<li>4. Straight Angle<\/li>\n<li>5. Reflex Angle<\/li>\n<\/ul>\n<ol>\n<li>Complementary Angles<\/li>\n<li>Supplementary Angles<\/li>\n<li>Angle Bisector<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"angles\"><\/span>Angles<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>When two rays merge with a common endpoint and the angle is set. The two segments of an angle are \u201csides\u201d and \u201cvertex.\u201d The side can be classified into terminal sides and initial sides (or vertical surfaces).<\/p>\n<h4><span class=\"ez-toc-section\" id=\"parts-of-angles\"><\/span><strong>Parts of Angles<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ol>\n<li><strong>Vertex:<\/strong> Point wherever the arms meet.<\/li>\n<li><strong>Arms:<\/strong> Two straight line segments set of a vertex.<\/li>\n<li><strong>Angle:<\/strong> If a ray is rotated around its endpoint, the measure of its rotation is known as the angle between its initial and final state.<\/li>\n<\/ol>\n<h4><span class=\"ez-toc-section\" id=\"classification-of-angles\"><\/span><strong>Classification of Angles<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Angles can be categorized based on two main kinds-<\/p>\n<ol>\n<li>Magnitude<\/li>\n<li>Rotation<\/li>\n<\/ol>\n<h4><span class=\"ez-toc-section\" id=\"types-of-angles\"><\/span><strong>Types of Angles<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ol>\n<li><strong>Acute Angles-<\/strong> An angle that lies between 0 degrees and 90 degrees (0\u00b0 and 90\u00b0) is known as an Acute Angle. In simple words- an acute angle is one that is less than 90\u00b0 (90 degrees).<\/li>\n<li><strong>Obtuse Angles- <\/strong>This angle is the opposite of an acute angle. It is the angle that lies between 90 degrees, and 180 degrees (90\u00b0 and 180\u00b0) is known as an Obtuse Angle. In simple words, an obtuse angle is greater than (90\u00b0) 90 degrees and less than 180 degrees (180\u00b0).<\/li>\n<li><strong>Right Angles-<\/strong> A right angle is perpetually equivalent to 90\u00b0 (90 degrees). Any angle less than 90 degrees (90\u00b0) is an acute angle, whereas any angle greater than 90\u00b0 is an obtuse angle.<\/li>\n<li><strong>Straight Angles-<\/strong> When measured, a straight angle is 180\u00b0 (180 degrees). It looks like a straight line because the angle between the arms is 180\u00b0.<\/li>\n<li><strong>Reflex Angles- <\/strong>Any angle with a measure that is greater than 180\u00b0 though less than 360\u00b0 (which corresponds with zero degrees) is a reflex angle.<\/li>\n<li><strong>Full Rotation- <\/strong>An angle equivalent to 360\u00b0 is known as full rotation or full angle. It is set when one of the arms carries a complete rotation to set an angle.<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"interior-and-exterior-of-an-angle\"><\/span><strong>Interior and Exterior of An Angle<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h4><span class=\"ez-toc-section\" id=\"interior-of-an-angle\"><\/span><strong>Interior of An Angle<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>The area between the rays makes an angle and prolonging away from the vertex to eternity.<\/p>\n<p>In simple words, An angle inside a frame, between two connected sides.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"the-exterior-of-an-angle\"><\/span><strong>The exterior of An Angle<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>It is the angle between any side of a shape and a line enlarged from the next side.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"congruent-angles\"><\/span><strong>Congruent Angles<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Congruent Angles have the same angle, whether in degrees or radians. Congruent Angles don&#8217;t have to point in the same direction. On similar sized lines, it is just the same angle.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"the-measure-of-an-angle\"><\/span><strong>The Measure of An Angle<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>An angle measure can be described as measuring an angle determined by the two rays or arms at a usual vertex. Angles are measured in degrees (\u00b0), applying a protractor.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"axioms-and-theorems\"><\/span><strong>Axioms and Theorems<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Axioms:<\/strong> We expect to be true without proof is known as an axiom.<\/p>\n<p><strong>Theorems:<\/strong> A mathematical description that we understand is true, which has a proof is a theorem.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"complementary-angles\"><\/span><strong>Complementary Angles<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>When the total of two angles is 90\u00b0, then the angles are called the complementary angles. In simple words, if two angles sum up to make a right angle, then these angles are indicated as complementary angles. We can say that the two angles complement each other.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"facts-of-complementary-angles\"><\/span><strong>Facts of Complementary Angles<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>Two right angles will not complement each other.<\/li>\n<li>Two obtuse angles will not complement each other.<\/li>\n<li>Two complementary angles can be acute, but vice versa is impossible.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"supplementary-angles\"><\/span><strong>Supplementary Angles<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>When the total of two angles is 180 degrees (180\u00b0), the angles are called the supplementary angles. In simple words, if two angles sum up to make a straight angle, then those angles are indicated as supplementary angles.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"angle-bisector\"><\/span><strong>Angle Bisector<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>&#8220;Bisect&#8221; anticipates dividing into two equal parts. Angle Bisector means a line that divides an angle into two similar angles.<\/p>\n<p><a href=\"https:\/\/cbse.gov.in\/\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Know about CBSE Board<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We will learn about the Lines and Angles in RD Sharma Chapter 8 Class 9 Maths Exercise 8.1 Solutions. The exercise is all about the Types of Angles, Axioms &amp; Theorems, Angle Bisector, Congruent Angles, etc. To make the concepts easy for the students, we have provided the exercise with easy solutions, which helps them &#8230; <a title=\"RD Sharma Chapter 8 Class 9 Maths Exercise 8.1 Solutions\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-chapter-8-class-9-maths-exercise-8-1-solutions\/\" aria-label=\"More on RD Sharma Chapter 8 Class 9 Maths Exercise 8.1 Solutions\">Read more<\/a><\/p>\n","protected":false},"author":241,"featured_media":71969,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2985,2917,73719,73411],"tags":[3081,3086,3085],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/71968"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/241"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=71968"}],"version-history":[{"count":3,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/71968\/revisions"}],"predecessor-version":[{"id":73412,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/71968\/revisions\/73412"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/71969"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=71968"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=71968"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=71968"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}