{"id":287,"date":"2022-04-13T10:34:26","date_gmt":"2022-04-13T10:34:26","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=287"},"modified":"2024-10-22T05:04:28","modified_gmt":"2024-10-22T05:04:28","slug":"o-2-triangle-angle-sum-theorem","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/o-2-triangle-angle-sum-theorem\/","title":{"rendered":"O.2 Triangle Angle-Sum Theorem"},"content":{"rendered":"\n

Triangle angle-sum Theorem<\/strong><\/h2>\n\n\n\n

Key Notes :<\/p>\n\n\n\n

The sum of the interior angle measures of a triangle is 180\u00b0.<\/strong><\/p>\n\n\n\n

A triangle is the smallest polygon that has three sides and three interior angles. In this article, we are going to discuss the angle sum property<\/p>\n\n\n\n

Angle Sum Property of a Triangle Theorem<\/h3>\n\n\n\n

In the given triangle, \u2206ABC, AB, BC, and CA represent three sides. A, B and C are the three vertices and \u2220ABC, \u2220BCA and \u2220CAB are three interior angles of \u2206ABC.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

Angle sum property of triangle states that the sum of interior angles of a triangle is 180\u00b0.<\/p>\n\n\n\n

Proof: <\/strong><\/p>\n\n\n\n

Consider a \u2206ABC, as shown in the figure below. To prove the above property of triangles, draw a line PQ parallel to the side BC of the given triangle.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

Since PQ is a straight line, it can be concluded that:<\/p>\n\n\n\n

\u2220PAB + \u2220BAC + \u2220QAC = 180\u00b0 \u2026\u2026\u2026(1)<\/p>\n\n\n\n

Since PQ||BC and AB, AC are transversals,<\/p>\n\n\n\n

Therefore, \u2220QAC = \u2220ACB (a pair of alternate angles)<\/p>\n\n\n\n

Also, \u2220PAB = \u2220CBA (a pair of alternate angles)<\/p>\n\n\n\n

Substituting the value of \u2220QAC and \u2220PAB in equation (1),<\/p>\n\n\n\n

\u2220ACB + \u2220BAC + \u2220CBA= 180\u00b0<\/p>\n\n\n\n

Thus, the sum of the interior angles of a triangle is 180\u00b0.<\/p>\n\n\n\n

Learn with an example<\/strong><\/p>\n\n\n\n

\n
\n

The diagram shows a triangle<\/strong><\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

What is the value of Y ?<\/strong><\/p>\n\n\n\n

Y =_________\u00b0<\/p>\n<\/div><\/div>\n\n\n\n

First, look at the interior angle measures in the triangle.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

Set the sum of the interior angle measures of the triangle equal to 180\u00b0. Solve for Y.<\/p>\n\n\n\n

68\u00b0 + Y + 49\u00b0 = 180\u00b0<\/p>\n\n\n\n

Y + 117\u00b0 = 180\u00b0 Combine like terms<\/p>\n\n\n\n

Y = 63\u00b0 Subtract 117\u00b0 from both sides<\/p>\n\n\n\n

So , Y = 63\u00b0<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

The diagram shows a triangle<\/strong><\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

What is the value of X ?<\/strong><\/p>\n\n\n\n

Y =_________\u00b0<\/p>\n<\/div><\/div>\n\n\n\n

First, look at the interior angle measures in the triangle.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

Set the sum of the interior angle measures of the triangle equal to 180\u00b0. Solve for X.<\/p>\n\n\n\n

30\u00b0 + 74\u00b0 + X = 180\u00b0<\/p>\n\n\n\n

X+ 104\u00b0 = 180\u00b0 Combine like terms<\/p>\n\n\n\n

X = 76\u00b0 Subtract 104\u00b0 from both sides<\/p>\n\n\n\n

So , X = 76\u00b0<\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

The diagram shows a triangle.<\/strong><\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

What is the value of  Y ?<\/strong><\/p>\n\n\n\n

Y =_________\u00b0<\/p>\n<\/div><\/div>\n\n\n\n

First, look at the interior angle measures in the triangle.<\/p>\n\n\n

\n
\"\"<\/figure><\/div>\n\n\n

Set the sum of the interior angle measures of the triangle equal to 180\u00b0. Solve for Y.<\/p>\n\n\n\n

48\u00b0 + Y + 44\u00b0 = 180\u00b0<\/p>\n\n\n\n

Y + 92\u00b0 = 180\u00b0 Combine like terms<\/p>\n\n\n\n

Y = 88\u00b0 Subtract 92\u00b0 from both sides<\/p>\n\n\n\n

So , Y = 88\u00b0<\/p>\n<\/div><\/div>\n\n\n\n

let’s practice!<\/p>\n\n\n\n

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

Triangle angle-sum Theorem Key Notes : The sum of the interior angle measures of a triangle is 180\u00b0. A triangle is the smallest polygon that has three sides and three interior angles. In this article, we are going to discuss the angle sum property Angle Sum Property of a Triangle Theorem In the given triangle, \u2206ABC, AB,Continue reading “O.2 Triangle Angle-Sum Theorem”<\/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-287","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/287","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=287"}],"version-history":[{"count":10,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/287\/revisions"}],"predecessor-version":[{"id":14226,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/287\/revisions\/14226"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=287"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}