{"id":352,"date":"2022-04-13T10:45:40","date_gmt":"2022-04-13T10:45:40","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=352"},"modified":"2025-01-10T09:47:49","modified_gmt":"2025-01-10T09:47:49","slug":"r-11-angles-in-inscribed-quadrilaterals","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/r-11-angles-in-inscribed-quadrilaterals\/","title":{"rendered":"R.11 Angles in inscribed quadrilaterals"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Angles in inscribed quadrilaterals<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-aae0d72b0df05b1a7d05750bd97517d2\" style=\"color:#74008b\"><strong>Key Notes :<\/strong><\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-9afe9342ee7786c6314e97bf6b9b6351\" style=\"color:#000060\"><strong>1. Definition<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">An <strong>inscribed quadrilateral<\/strong> is a four-sided polygon whose vertices all lie on the circumference of a circle. It is also called a <strong>cyclic quadrilateral<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-bae0433b63ba7b3844b85ce97fcf24bf\" style=\"color:#000060\"><strong>2. Properties of Inscribed Quadrilaterals<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\"><strong>Opposite Angles are Supplementary:<\/strong><br>The sum of the measures of opposite angles in an inscribed quadrilateral is always 180<sup>0<\/sup>.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"475\" height=\"51\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2025\/01\/image.png\" alt=\"\" class=\"wp-image-17387\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2025\/01\/image.png 475w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2025\/01\/image-300x32.png 300w\" sizes=\"auto, (max-width: 475px) 100vw, 475px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Exterior Angle Property:<\/strong>The exterior angle of an inscribed quadrilateral is equal to the interior opposite angle.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"178\" height=\"44\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2025\/01\/image-1.png\" alt=\"\" class=\"wp-image-17388\"\/><\/figure><\/div>\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-ba0eb9da906f958db78d1cf9a3fd523f\" style=\"color:#000060\"><strong>3. Cyclic Quadrilateral Conditions<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\">A quadrilateral can be inscribed in a circle if:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>The opposite angles are supplementary.<\/li>\n\n\n\n<li>The perpendicular bisectors of the sides of the quadrilateral meet at the center of the circumscribing circle.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-06ca9c7f5d65bf4630d62aabde3d62a6\" style=\"color:#000060\"><strong>4. Theorems Related to Inscribed Quadrilaterals<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\"><strong>Angle Sum Theorem:<\/strong><br>The sum of all angles in any quadrilateral is 360<sup>0<\/sup> .<br>For an inscribed quadrilateral:<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"323\" height=\"40\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2025\/01\/image-2.png\" alt=\"\" class=\"wp-image-17389\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2025\/01\/image-2.png 323w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2025\/01\/image-2-300x37.png 300w\" sizes=\"auto, (max-width: 323px) 100vw, 323px\" \/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>Converse of the Opposite Angle Theorem:<\/strong>If the sum of opposite angles of a quadrilateral is 180<sup>0<\/sup>, then the quadrilateral can be inscribed in a circle.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-b101186f31bc907f844057651eb18077\" style=\"background-color:#bef1e8\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-bac367e03fe8dace02b57f25c6615ffc\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-43c3cf747733c7a749d92aa8f30b7def\" style=\"color:#b00012\"><strong>\u27a1\ufe0f What&nbsp;is&nbsp;\u2220D?<\/strong><\/p>\n\n\n<div class=\"wp-block-image size-full\">\n<figure class=\"aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/d-1.png\" alt=\"\" class=\"wp-image-11806\" style=\"width:370px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/d-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/d-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/d-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>\u2220D=_____ \u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-c027a0ef54b0f71bc7166c4b77fe72af\">Look&nbsp;at the&nbsp;diagram:<\/p>\n\n\n<div class=\"wp-block-image size-full\">\n<figure class=\"aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/d__1_-removebg-preview.png\" alt=\"\" class=\"wp-image-11808\" style=\"width:429px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/d__1_-removebg-preview.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/d__1_-removebg-preview-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/d__1_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Since&nbsp;DEFG&nbsp;is an inscribed quadrilateral,&nbsp;\u2220F&nbsp;and&nbsp;\u2220D&nbsp;are supplementary. Write an equation setting the sum of their measures equal to&nbsp;180\u00b0,&nbsp;and solve for&nbsp;\u2220D.<\/p>\n\n\n\n<p>\u2220F+\u2220D=180\u00b0<\/p>\n\n\n\n<p><strong>108\u00b0<\/strong>+\u2220D=180\u00b0            Plug&nbsp;in&nbsp;\u2220F=108\u00b0<\/p>\n\n\n\n<p>\u2220D=72\u00b0                    Subtract&nbsp;108\u00b0&nbsp;from both&nbsp;sides<\/p>\n\n\n\n<p>\u2220D is 72\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-30ec35d3e22f91e46476cc6823e9fd73\" style=\"background-color:#f1eea2\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-6ae26332162a28c7e7e43fb83a2509f0\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-8a7bd0928aac1d371c62ba882aae619f\" style=\"color:#b00012\"><strong>\u27a1\ufe0f What&nbsp;is&nbsp;\u2220H?<\/strong><\/p>\n\n\n<div class=\"wp-block-image size-full\">\n<figure class=\"aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/d-2.png\" alt=\"\" class=\"wp-image-11811\" style=\"width:389px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/d-2.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/d-2-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/d-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>\u2220H=______ \u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>Look&nbsp;at the&nbsp;diagram:<\/p>\n\n\n<div class=\"wp-block-image size-full\">\n<figure class=\"aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-17.png\" alt=\"\" class=\"wp-image-11812\" style=\"width:394px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-17.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-17-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-17-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Since&nbsp;FGHI&nbsp;is an inscribed quadrilateral,&nbsp;\u2220F&nbsp;and&nbsp;\u2220H&nbsp;are supplementary. Write an equation setting the sum of their measures equal to&nbsp;180\u00b0,&nbsp;and solve for&nbsp;\u2220H.<\/p>\n\n\n\n<p>\u2220F+\u2220H=180\u00b0<\/p>\n\n\n\n<p><strong>86\u00b0<\/strong>+\u2220H=180\u00b0             Plug&nbsp;in&nbsp;\u2220F=86\u00b0<\/p>\n\n\n\n<p>\u2220H=94\u00b0                   Subtract&nbsp;86\u00b0&nbsp;from both&nbsp;sides<\/p>\n\n\n\n<p>\u2220H is 94\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-b35b5bddd033e4a863aaab4b12ac92ff\" style=\"background-color:#c7faf5\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-c70fa5250e536b4747dc187fcb675af7\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-74f9e376786cc43d9f8db1670e0a0784\" style=\"color:#b00012\"><strong>\u27a1\ufe0f What&nbsp;is&nbsp;\u2220G?<\/strong><\/p>\n\n\n<div class=\"wp-block-image size-full\">\n<figure class=\"aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/d-3.png\" alt=\"\" class=\"wp-image-11816\" style=\"width:393px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/d-3.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/d-3-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/d-3-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>\u2220G=________ \u00b0<\/p>\n<\/div><\/div>\n\n\n\n<p>Look&nbsp;at the&nbsp;diagram:<\/p>\n\n\n<div class=\"wp-block-image size-full\">\n<figure class=\"aligncenter is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-18.png\" alt=\"\" class=\"wp-image-11817\" style=\"width:417px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-18.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-18-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-18-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Since&nbsp;GHIJ&nbsp;is an inscribed quadrilateral,&nbsp;\u2220I&nbsp;and&nbsp;\u2220G&nbsp;are supplementary. Write an equation setting the sum of their measures equal to&nbsp;180\u00b0,&nbsp;and solve for&nbsp;\u2220G.<\/p>\n\n\n\n<p>\u2220I+\u2220G=180\u00b0<\/p>\n\n\n\n<p><strong>102\u00b0<\/strong>+\u2220G=180\u00b0             Plug&nbsp;in&nbsp;\u2220I=102\u00b0<\/p>\n\n\n\n<p>\u2220G=78\u00b0                     Subtract&nbsp;102\u00b0&nbsp;from both&nbsp;sides<\/p>\n\n\n\n<p>\u2220G is 78\u00b0.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#d90000\"><strong>let&#8217;s practice!<\/strong><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/84491\/618\/825\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-122.png\" alt=\"\" class=\"wp-image-7355\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-122.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-122-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-122-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/84598\/603\/218\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-141.png\" alt=\"\" class=\"wp-image-7356\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-141.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-141-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-141-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Angles in inscribed quadrilaterals Key Notes : 1. Definition An inscribed quadrilateral is a four-sided polygon whose vertices all lie on the circumference of a circle. It is also called a cyclic quadrilateral. 2. Properties of Inscribed Quadrilaterals Opposite Angles are Supplementary:The sum of the measures of opposite angles in an inscribed quadrilateral is always<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/r-11-angles-in-inscribed-quadrilaterals\/\">Continue reading <span class=\"screen-reader-text\">&#8220;R.11 Angles in inscribed quadrilaterals&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-352","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/352","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=352"}],"version-history":[{"count":16,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/352\/revisions"}],"predecessor-version":[{"id":17391,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/352\/revisions\/17391"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=352"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}