[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-143225-105":59,"doc-detail-143225-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","angles-in-polygons-workout-and-answers","Angles in Polygons - Workout and Answers","","A learning resource focused on angle geometry for polygons, covering how to measure angles in degrees, interpret angles around a point, and use key facts such as the sum of interior angles for triangles and general polygons. It trains learners through progressively structured workout questions, including missing angles, sums of interior angles, determining the number of sides from angle sums, and calculating interior and exterior angles of regular polygons. An answers section provides worked outcomes for selected problems.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/angles-in-polygons-workout-and-answers/143225/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/angles-in-polygons-workout-and-answers/143225.png","ImageObject",300,407,{"name":92,"@type":93},"Olivia Brown","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-09-20","2026-08-25",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you measure an angle in degrees and what do 45° and 90° represent?","Question",{"text":112,"@type":113},"An angle is formed when two lines meet at a common point, and its size is measured as the degree of turn between the lines. Values like 45° and 90° indicate the turning amounts in degrees.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What is the sum of the interior angles of a triangle and how is it used?",{"text":117,"@type":113},"The interior angles of a triangle sum to 180°. This rule is used to find missing angle values in triangle-based diagrams.",{"name":119,"@type":110,"acceptedAnswer":120},"How do you calculate interior and exterior angles of regular polygons?",{"text":121,"@type":113},"For regular polygons, each interior angle depends on the number of sides, and each exterior angle is also fixed. The worksheet practices both methods, including computing exterior angles and determining the number of sides from given angles.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},143225,1787693773,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":39,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":129,"read_time":46},16904993612988,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","# Angles in polygons\n\nAn angle is created when two lines meet at a common point.To measure an angle,we measure the degree of turn between these two lines eg 90°,45°.  \nAngles can measure from O to 360 degrees (a fullcircle).  \n@westminstermath+998944905775  \n60°60090°30°60°60°  \nThe sum of the angles inside both regular and irregular polygonsis the same eg in a triangle they equal 180°.  \n# Angles in Polygons\n\nName:_                 \nFind the value of the angles in the polygons.  \nABCD is a parallelogramCB60°DAL ADC=  \nRSTU is a trapezium  \nNOPQR is a regular pentagon  \nS  \nN  \nR  \nR  \n0  \nUL  \nT  \np  \nQ  \n∠URS =_____  \nL RQP=____  \nExamples  \n@westminstermath+998944905775  \n## Workout\n\nQuestion 1:Find the missing angle in each irregular polygon  \n(b)  \n(a)  \n(c)  \n(d)  \n(e)  \n(f)  \n(g)  \n(h)  \n(i)  \n(j)  \n(k)  \n(1)  \n# Angles in Polygons\n\n(n)  \nQuestion 2:Work out the sum of the interior angles for polygons with  \n(d)45 sides  \n(a)10 sides  \n(b)14 sides  \n(c)20 sides  \n(e)50 sides  \n(f)80 sides  \n(g)100 sides  \n(h)200 sides  \nQuestion 3:Work out the number of sides of polygons with these sum of interior angles  \n(a)1260°  \n(c)3960°  \n(d)5040°  \n(b)2880°  \n(e)12240°  \n(f)15840°  \n(g)2340°  \n(h)89640°  \nQuestion 4:Each of the polygons below are regular:  \nCalculate the size of each interior angle,x.  \n(a)  \n(b)  \n〔c〕  \nregular pentagon  \nregular hexagon  \nregular octagon  \n(f)  \n(d)  \n(e)  \nregular nonagon  \nregular decagon  \nAngles in Polygons  \nQuestion 5:Calculate the size of each interior angle in regular polygons with  \n(b)20 sides  \n(c)24 sides  \n(a)15 sides  \n(d)30 sides  \n(e)36 sides  \n(f)40 sides  \n(g)50 sides  \n(h)60 sides  \n(1)72 sides  \n(1)80 sides  \n(k)90 sides  \n(1)100 sides  \nQuestion 6:Each of the polygons below are regular.Calculate the size of each exterior angle,y.  \n〔a〕  \n(b)  \n(c)  \nregular pentagon  \nregular hexagon  \nregular octagon  \n(d)  \n(e)  \n(f)  \nregular decagon  \nregular nonagon  \nregular dodecagon  \nQuestion 7:Calculate the size of each exterior angle in regular polygons with  \n(a)15 sides  \n(c)20 sides  \n(d)24 sides  \n(b)18sides  \n(e)30 sides  \n(1)36sides  \n(g)40 sides  \n(h)45 sides  \n(i)60 sides  \n(j)72 sides  \n(k)90 sides  \n(1)200 sides  \nQuestion 8:Shown below is one interior angle from regular polygons.Calculate how many sides the polygons have.  \n〔a〕  \n(b)  \n(c)  \n(d)  \n(e)  \n(f)  \n# Angles in Polvgons\n\n## Apply\n\nQuestion 1:In each diagram below,two regular polygons are shown.Calculate x.  \n(a)  \n(b)  \n(c)  \n(d)  \nQuestion 2:Shown is a regular pentagon.Findy.  \nQuestion 3:Aregular polygon has 18 sides.Calculate the size of each interior angle.  \nQuestion 4:A regular polygon has 30 sides.Calculate the size of each interior angle.  \nQuestion 5:Explain why this cannot be an interior angle from regular polygons.  \nQuestion 6:A polygon has an interior angle that is five times larger than the exterior angle.How many sides does it have?  \nQuestion 7:Explain why regular hexagons tessellate.  \nQuestion 8:Explain why regular pentagons do not tessellate.  \n@westminstermath+998944905775  \n## Answers\n\n1.Each exterior angle of a regular polygon is 30°.  \nWork out the number of sides of the polygon.  \n                                       (2 marks)  \n2.  \nDiagram NOT  \naccurately drawn  \nWork out the size of an exterior angle of a regular pentagon.  \n……   ……  \n                                  (2marks)  \n3.  \nDiagram NOT  \naccurately drawn  \nCalculate the size of the exterior angle of a regular hexagon.  \n4.  The size of each exterior angle of a regular polygon is 40°.  \nWork out the number of sides of the regular polygon.(2 marks)  \n5.  The size of each interior angle of a regular polygon is 156°.Work out the number of sides of the polygon.  \n(3marks)  \n6.  Here is a regular polygon with 9 sides.  \nDiagram NOT accurately drawn  \nWork out the size of an exterior angle.  \n@westminstermath+998944905775  \n……………………….  \nDiagram NOT accurately drawn  \n(a)Work out the size of each interior angle of a regular oct","cbCaib5hXDGaBeCd","https://ap.wps.com/l/cbCaib5hXDGaBeCd","pdf",964975,"English","# Angles in Polygons\n## Workout\n## Answers","[{\"question\":\"How do you measure an angle in degrees and what do 45° and 90° represent?\",\"answer\":\"An angle is formed when two lines meet at a common point, and its size is measured as the degree of turn between the lines. Values like 45° and 90° indicate the turning amounts in degrees.\"},{\"question\":\"What is the sum of the interior angles of a triangle and how is it used?\",\"answer\":\"The interior angles of a triangle sum to 180°. This rule is used to find missing angle values in triangle-based diagrams.\"},{\"question\":\"How do you calculate interior and exterior angles of regular polygons?\",\"answer\":\"For regular polygons, each interior angle depends on the number of sides, and each exterior angle is also fixed. The worksheet practices both methods, including computing exterior angles and determining the number of sides from given angles.\"}]","Angles in Polygons - Workout and Answers | PDF"]