{"id":10915,"date":"2026-11-02T02:04:39","date_gmt":"2026-11-02T02:04:39","guid":{"rendered":"https:\/\/kapdec.com\/help\/?p=10915"},"modified":"2026-11-02T02:04:39","modified_gmt":"2026-11-02T02:04:39","slug":"angles-triangles","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/angles-triangles\/","title":{"rendered":"Angles &#038; Triangles"},"content":{"rendered":"<div class=\"article-watermark-wrapper\">\n<div style=\"position: relative; z-index: 1;\">\n<p style=\"font-family: Arial, Helvetica, Calibri, sans-serif; font-size: 9pt; color: #444444;\">KAPDEC&reg; | Elite STEM Learning Platform | <a href=\"https:\/\/kapdec.com\" target=\"_blank\" rel=\"noopener noreferrer\" style=\"color: #444444; text-decoration: underline;\">https:\/\/kapdec.com<\/a><\/p>\n<hr \/>\n<h2><strong>Unit<\/strong>: Geometry<\/h2>\n<h3><strong>Chapter<\/strong>: Angles &amp; Triangles<\/h3>\n<p><strong>Reference<\/strong>: \u2013 <em>Introduction to Angles, Arms and Vertex, Naming of Angles, Interior &amp; Exterior of an Angle, Types of Angles (Acute, Right, Obtuse, Straight, Reflex, Zero, Complete), Triangles and Their Classification (By Sides and By Angles), Angle Sum Property of a Triangle<\/em><\/p>\n<p>After studying this chapter, you should be able to understand:<\/p>\n<ul>\n<li>Introduction to Angles &amp; Their Formation<\/li>\n<li>Arms and Vertex of an Angle<\/li>\n<li>Naming Angles (Three-Letter and Vertex Names)<\/li>\n<li>Interior and Exterior of an Angle<\/li>\n<li>Types of Angles and Their Measures<\/li>\n<li>Classification of Triangles by Sides (Equilateral, Isosceles, Scalene)<\/li>\n<li>Classification of Triangles by Angles (Acute, Right, Obtuse)<\/li>\n<li>Angle Sum Property of a Triangle (180\u00b0)<\/li>\n<\/ul>\n<p><strong>Geometry Basic Elements: Angles<\/strong><\/p>\n<p>\u00a0<\/p>\n<p>An angle is a combination of two\u00a0<a href=\"https:\/\/www.cut-the-knot.org\/WhatIs\/WhatIsLine.shtml\" target=\"_blank\" rel=\"noopener\">rays<\/a>\u00a0(half-lines) with a common endpoint. The latter is known as the\u00a0vertex\u00a0of the angle and the rays as the\u00a0sides, sometimes as the\u00a0legs\u00a0and sometimes as the\u00a0arms\u00a0of the angle.<\/p>\n<p>Look at the figures below-<\/p>\n<p><div class=\"kapdec-figure-wrapper\" style=\"display: inline-block; max-width: 100%; vertical-align: top;\"><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"142\" src=\"https:\/\/app.kapdec.com\/questions-images\/3bOogkU74AFp1790076812.png?time=1790076813\" width=\"354\"><\/p>\n<p class=\"kapdec-figure-source\" style=\"font-family: Arial, Helvetica, Calibri, sans-serif; font-size: 8pt; color: #666666; text-align: right; margin: 4px 0 12px 0;\">Source: Kapdec.com<\/p>\n<\/div>\n<p> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/p>\n<p>Each of the figures above show real life examples of angles which we see in daily life.<\/p>\n<p>\u00a0<\/p>\n<p><strong>Types of Angles:<\/strong><\/p>\n<p><strong>Right Angle:<\/strong> when two lines segments or rays intersect such that the angle formed between them is 90 degree, then it is called a \u201cRight Angle\u201d.<\/p>\n<p><div class=\"kapdec-figure-wrapper\" style=\"display: inline-block; max-width: 100%; vertical-align: top;\"><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"112\" src=\"https:\/\/app.kapdec.com\/questions-images\/0nvoqfQroiZF1790076812.png?time=1790076813\" width=\"228\"><\/p>\n<p class=\"kapdec-figure-source\" style=\"font-family: Arial, Helvetica, Calibri, sans-serif; font-size: 8pt; color: #666666; text-align: right; margin: 4px 0 12px 0;\">Source: Kapdec.com<\/p>\n<\/div>\n<p> \u00a0<\/p>\n<p>\u00a0<\/p>\n<p><strong>Acute Angle:<\/strong> Any angle which is smaller than right angle is an acute angle.<\/p>\n<p><div class=\"kapdec-figure-wrapper\" style=\"display: inline-block; max-width: 100%; vertical-align: top;\"><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"113\" src=\"https:\/\/app.kapdec.com\/questions-images\/idTC4Bs3cE6s1790076812.png?time=1790076813\" width=\"262\"><\/p>\n<p class=\"kapdec-figure-source\" style=\"font-family: Arial, Helvetica, Calibri, sans-serif; font-size: 8pt; color: #666666; text-align: right; margin: 4px 0 12px 0;\">Source: Kapdec.com<\/p>\n<\/div>\n<p>\u00a0<\/p>\n<p><strong>Obtuse Angle: <\/strong>When an angle is larger than 90 Degrees (right angle) but smaller than 180 Degree, (a straight angle), then it is called as an obtuse angle<\/p>\n<p>Reflex Angle: A reflex angle is larger than a straight angle,<\/p>\n<p><div class=\"kapdec-figure-wrapper\" style=\"display: inline-block; max-width: 100%; vertical-align: top;\"><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"131\" src=\"https:\/\/app.kapdec.com\/questions-images\/ooCYo72pxAle1790076813.png?time=1790076814\" width=\"627\"><\/p>\n<p class=\"kapdec-figure-source\" style=\"font-family: Arial, Helvetica, Calibri, sans-serif; font-size: 8pt; color: #666666; text-align: right; margin: 4px 0 12px 0;\">Source: Kapdec.com<\/p>\n<\/div>\n<p>The portion that lies in between the two rays is called the interior of the angle. In naming an angle, the vertex is always written at a point where two rays meet (intersection point).And is denoted in Capital Letters.<\/p>\n<p>For example, the angle made by ladder with the floor or with the wall is an example of an acute angle.<\/p>\n<p><div class=\"kapdec-figure-wrapper\" style=\"display: inline-block; max-width: 100%; vertical-align: top;\"><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"145\" src=\"https:\/\/app.kapdec.com\/questions-images\/Gl5E3VhGs47B1790076813.png?time=1790076814\" width=\"149\"><\/p>\n<p class=\"kapdec-figure-source\" style=\"font-family: Arial, Helvetica, Calibri, sans-serif; font-size: 8pt; color: #666666; text-align: right; margin: 4px 0 12px 0;\">Source: Kapdec.com<\/p>\n<\/div>\n<p> \u00a0<\/p>\n<p>\u00a0<\/p>\n<p><strong>Measuring Angles:<\/strong><\/p>\n<p>We use a protractor to measure angles. The picture of a protractor looks like below:<\/p>\n<p><div class=\"kapdec-figure-wrapper\" style=\"display: inline-block; max-width: 100%; vertical-align: top;\"><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"163\" src=\"https:\/\/app.kapdec.com\/questions-images\/QSMBcwev4d4r1790076813.png?time=1790076814\" width=\"328\"><\/p>\n<p class=\"kapdec-figure-source\" style=\"font-family: Arial, Helvetica, Calibri, sans-serif; font-size: 8pt; color: #666666; text-align: right; margin: 4px 0 12px 0;\">Source: Kapdec.com<\/p>\n<\/div>\n<p> \u00a0<\/p>\n<p>\u00a0<\/p>\n<p>The unit used to measure an angle is called degree. One revolution or complete angle is divided into 360 equal parts. Each part is called a degree. So three hundred sixty degree is written as 360 \u00b0<\/p>\n<p>The protractor is divided into 180 equal parts. Its marking is like it starts from on left side and ends at the right side and Vice versa.<\/p>\n<p><div class=\"kapdec-figure-wrapper\" style=\"display: inline-block; max-width: 100%; vertical-align: top;\"><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"142\" src=\"https:\/\/app.kapdec.com\/questions-images\/hzv5c6S7yHlF1790076813.png?time=1790076814\" width=\"206\"><\/p>\n<p class=\"kapdec-figure-source\" style=\"font-family: Arial, Helvetica, Calibri, sans-serif; font-size: 8pt; color: #666666; text-align: right; margin: 4px 0 12px 0;\">Source: Kapdec.com<\/p>\n<\/div>\n<p>\u00a0<\/p>\n<p>Suppose you want to measure angle PQR, from above diagram.<\/p>\n<p>Following are the steps:<\/p>\n<ul>\n<li>Place the protractor such that its mid-point lies with end Q.<\/li>\n<li>The line segment QR should lie along the straight edge with the protractor.<\/li>\n<li>A protractor constitutes two scales. Always read the scale with mark coinciding with the straight line. So, in this case we will read lower scale.<\/li>\n<li>The other mark at P shows 50 \u00b0, so angle\u00a0 PQR=50 \u00b0<\/li>\n<\/ul>\n<p><div class=\"kapdec-figure-wrapper\" style=\"display: inline-block; max-width: 100%; vertical-align: top;\"><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"222\" src=\"https:\/\/app.kapdec.com\/questions-images\/2BX1mu1AScWw1790076814.png?time=1790076815\" width=\"413\"><\/p>\n<p class=\"kapdec-figure-source\" style=\"font-family: Arial, Helvetica, Calibri, sans-serif; font-size: 8pt; color: #666666; text-align: right; margin: 4px 0 12px 0;\">Source: Kapdec.com<\/p>\n<\/div>\n<p>\u00a0<\/p>\n<p>\u00a0<\/p>\n<p><!--kapdec-footer-start--><\/p>\n<style>.kapdec-article-footer{font-family:Arial,Helvetica,Calibri,sans-serif;color:#444;}.kapdec-footer-grid{display:flex;align-items:stretch;border:1px solid #e5e7eb;border-radius:6px;overflow:hidden;}.kapdec-footer-left,.kapdec-qr-block{flex:1 1 50%;width:50%;box-sizing:border-box;min-width:0;}.kapdec-footer-left{padding:22px 28px;border-right:1px solid #e5e7eb;}.kapdec-citation-block{line-height:1.6;font-size:9pt;color:#333;margin:0;}.kapdec-citation-block p{margin:0 0 10px 0;}.kapdec-citation-block a{color:#0066cc;text-decoration:underline;}.kapdec-copyright-block{margin-top:18px;padding-top:14px;border-top:1px solid #e5e7eb;font-size:7.5pt;color:#777;line-height:1.55;text-align:left;}.kapdec-copyright-block p{margin:0 0 5px 0;}.kapdec-qr-block{padding:22px 28px;display:flex;flex-direction:column;align-items:center;justify-content:center;text-align:center;}.kapdec-qr-label{margin:0 0 8px 0;font-size:8.5pt;font-weight:600;color:#444;line-height:1.35;letter-spacing:.02em;}.kapdec-qr-url{margin:0 0 14px 0;font-size:7.5pt;line-height:1.4;color:#777;word-break:break-word;max-width:100%;}.kapdec-qr-url a{color:#777;text-decoration:underline;}@media (max-width:640px){.kapdec-footer-grid{flex-direction:column;}.kapdec-footer-left,.kapdec-qr-block{width:100%;flex-basis:100%;border-right:none;}.kapdec-footer-left{border-bottom:1px solid #e5e7eb;}}<\/style>\n<div class=\"kapdec-article-footer\" style=\"margin-top: 28px; padding-top: 4px;\">\n<div class=\"kapdec-footer-grid\">\n<div class=\"kapdec-footer-left\">\n<div class=\"kapdec-citation-block\">\n<p>A Kapdec&reg; learning guide &#8211; Crafted by elite STEM mentors for ambitious learners.<\/p>\n<p><a href=\"https:\/\/kapdec.com\" target=\"_blank\" rel=\"noopener noreferrer\">Learn more at https:\/\/kapdec.com<\/a><\/p>\n<\/div>\n<div class=\"kapdec-copyright-block\">\n<p>Author: Kapdec | Publisher: Kapdec | Copyright: &copy; Kapdec. 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