{"id":224875,"date":"2025-06-03T14:41:51","date_gmt":"2025-06-03T14:41:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224875"},"modified":"2025-06-03T14:41:53","modified_gmt":"2025-06-03T14:41:53","slug":"geometry-name","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/03\/geometry-name\/","title":{"rendered":"Geometry NAME"},"content":{"rendered":"\n

Geometry NAME: WORKSHEET: Polygon Angle Measures PERIOD: DATE: Use the given information to complete the table. Round to the nearest tenth if necessary. # Sides Interior Angle Sum Measure of ONE INTERIOR Angle (Regular Polygon) Exterior Angle Sum Measure of ONE EXTERIOR Angle (Regular Polygon) 1) n 2) 14 3) 24 4) 17 5) 1080\u00b0 6) 900\u00b0 7) 5040\u00b0 8) 1620\u00b0 9) 150\u00b0 10) 120\u00b0 11) 156\u00b0 12) 10\u00b0 13) 7.2\u00b0 14) 90\u00b0 15) 5\u00b0<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To complete this Polygon Angle Measures Worksheet<\/strong>, we use the following key formulas:<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udd37 Key Formulas<\/strong>:<\/h3>\n\n\n\n
    \n
  1. Interior Angle Sum<\/strong> = (n – 2) \u00d7 180\u00b0<\/li>\n\n\n\n
  2. Measure of One Interior Angle (regular polygon)<\/strong> = [(n – 2) \u00d7 180\u00b0] \u00f7 n<\/li>\n\n\n\n
  3. Exterior Angle Sum<\/strong> = 360\u00b0 (Always true for any polygon)<\/li>\n\n\n\n
  4. One Exterior Angle (regular polygon)<\/strong> = 360\u00b0 \u00f7 n<\/li>\n\n\n\n
  5. To find n<\/strong> from an angle measure:\n
      \n
    • For interior angle<\/strong>:
      n=360180\u2212Interior\u00a0Anglen = \\frac{360}{180 – \\text{Interior Angle}}<\/li>\n\n\n\n
    • For exterior angle<\/strong>:
      n=360Exterior\u00a0Anglen = \\frac{360}{\\text{Exterior Angle}}<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n
      \n\n\n\n

      \ud83d\udd22 Completed Table<\/strong>:<\/h3>\n\n\n\n
      #<\/th>Sides (n)<\/th>Interior Angle Sum<\/th>One Interior Angle<\/th>Exterior Angle Sum<\/th>One Exterior Angle<\/th><\/tr><\/thead>
      1<\/td>n<\/td>(n – 2) \u00d7 180\u00b0<\/td>[(n – 2) \u00d7 180]\/n<\/td>360\u00b0<\/td>360\/n<\/td><\/tr>
      2<\/td>14<\/td>2160\u00b0<\/td>154.3\u00b0<\/td>360\u00b0<\/td>25.7\u00b0<\/td><\/tr>
      3<\/td>24<\/td>3960\u00b0<\/td>165\u00b0<\/td>360\u00b0<\/td>15\u00b0<\/td><\/tr>
      4<\/td>17<\/td>2700\u00b0<\/td>158.8\u00b0<\/td>360\u00b0<\/td>21.2\u00b0<\/td><\/tr>
      5<\/td>8<\/td>1080\u00b0<\/td>135\u00b0<\/td>360\u00b0<\/td>45\u00b0<\/td><\/tr>
      6<\/td>7<\/td>900\u00b0<\/td>128.6\u00b0<\/td>360\u00b0<\/td>51.4\u00b0<\/td><\/tr>
      7<\/td>30<\/td>5040\u00b0<\/td>168\u00b0<\/td>360\u00b0<\/td>12\u00b0<\/td><\/tr>
      8<\/td>11<\/td>1620\u00b0<\/td>147.3\u00b0<\/td>360\u00b0<\/td>32.7\u00b0<\/td><\/tr>
      9<\/td>12<\/td>1800\u00b0<\/td>150\u00b0<\/td>360\u00b0<\/td>30\u00b0<\/td><\/tr>
      10<\/td>9<\/td>1260\u00b0<\/td>140\u00b0<\/td>360\u00b0<\/td>40\u00b0<\/td><\/tr>
      11<\/td>15<\/td>2340\u00b0<\/td>156\u00b0<\/td>360\u00b0<\/td>24\u00b0<\/td><\/tr>
      12<\/td>36<\/td>6120\u00b0<\/td>170\u00b0<\/td>360\u00b0<\/td>10\u00b0<\/td><\/tr>
      13<\/td>50<\/td>8640\u00b0<\/td>172.8\u00b0<\/td>360\u00b0<\/td>7.2\u00b0<\/td><\/tr>
      14<\/td>4<\/td>360\u00b0<\/td>90\u00b0<\/td>360\u00b0<\/td>90\u00b0<\/td><\/tr>
      15<\/td>72<\/td>12600\u00b0<\/td>175\u00b0<\/td>360\u00b0<\/td>5\u00b0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
      \n\n\n\n

      \ud83d\udcd8 Explanation <\/strong><\/h3>\n\n\n\n

      This worksheet focuses on understanding the geometric relationships between a polygon’s number of sides and its interior and exterior angles.<\/p>\n\n\n\n

      To find the interior angle sum<\/strong> of any polygon, we use the formula (n\u22122)\u00d7180\u2218(n – 2) \\times 180^\\circ, because every polygon can be divided into (n\u22122)(n – 2) triangles. For example, a 14-gon has an interior angle sum of (14\u22122)\u00d7180=2160\u2218(14 – 2) \\times 180 = 2160^\\circ.<\/p>\n\n\n\n

      For regular polygons<\/strong> (where all sides and angles are equal), the measure of one interior angle<\/strong> is simply the total interior angle sum divided by the number of sides. Using the same 14-gon: 2160\u2218\u00f714\u2248154.3\u22182160^\\circ \\div 14 \\approx 154.3^\\circ.<\/p>\n\n\n\n

      All polygons, regardless of the number of sides, have an exterior angle sum of 360\u00b0<\/strong>. This is because exterior angles make one full turn around the polygon.<\/p>\n\n\n\n

      To find one exterior angle<\/strong> of a regular polygon, divide 360\u00b0 by the number of sides. For example, in a regular 24-gon, each exterior angle is 360\u2218\u00f724=15\u2218360^\\circ \\div 24 = 15^\\circ, and each interior angle is 180\u2218\u221215\u2218=165\u2218180^\\circ – 15^\\circ = 165^\\circ.<\/p>\n\n\n\n

      Sometimes, we\u2019re given the measure of one interior or exterior angle and must work backward to find the number of sides. For instance, if one interior angle is 156\u00b0, then the exterior angle is 180\u2218\u2212156\u2218=24\u2218180^\\circ – 156^\\circ = 24^\\circ, and n=360\u2218\u00f724\u2218=15n = 360^\\circ \\div 24^\\circ = 15 sides.<\/p>\n\n\n\n

      This table demonstrates how polygon properties are interconnected. Mastering these formulas enables students to quickly calculate unknown values and reinforces the importance of angle relationships in geometry.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      Geometry NAME: WORKSHEET: Polygon Angle Measures PERIOD: DATE: Use the given information to complete the table. Round to the nearest tenth if necessary. # Sides Interior Angle Sum Measure of ONE INTERIOR Angle (Regular Polygon) Exterior Angle Sum Measure of ONE EXTERIOR Angle (Regular Polygon) 1) n 2) 14 3) 24 4) 17 5) 1080\u00b0 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-224875","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224875","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=224875"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224875\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224875"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224875"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224875"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}