{"id":196,"date":"2022-04-13T08:41:18","date_gmt":"2022-04-13T08:41:18","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=196"},"modified":"2025-12-04T12:07:14","modified_gmt":"2025-12-04T12:07:14","slug":"l-2-central-angles","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/l-2-central-angles\/","title":{"rendered":"L.2 Central angles"},"content":{"rendered":"\n

Central angles<\/strong><\/h2>\n\n\n\n

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

\ud83d\udd35 What is a Central Angle?<\/strong><\/h3>\n\n\n\n

A central angle<\/strong> is an angle whose vertex is at the center<\/strong> of a circle.
Its rays<\/strong> (arms) point to the circumference<\/strong> of the circle.
\u27a1\ufe0f Example: Angle \u2220AOB in circle O.<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udd34 Central Angle and Arc Measure<\/strong><\/h3>\n\n\n\n

A central angle cuts an arc<\/strong> on the circle.
\ud83d\udccf The measure of a central angle = the measure of its intercepted arc.<\/strong>
\ud83d\udc49 If arc AB = 60\u00b0, then \u2220AOB = 60\u00b0<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udfe3 Central Angle Formula (Radians)<\/strong><\/h3>\n\n\n\n

If the arc length = s<\/em> and radius = r<\/em>
\ud83d\udc49 \u03b8 = s \/ r<\/strong> (in radians)<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udfe2 Full Circle Facts<\/strong><\/h3>\n\n\n\n

A circle has:
\ud83d\udd38 360\u00b0<\/strong> (degrees)
\ud83d\udd38 2\u03c0 radians<\/strong>
\ud83d\udc49 Central angles add up to 360\u00b0<\/strong>.<\/p>\n\n\n\n

\n\n\n\n

\ud83d\udfe1 Relationship With Inscribed Angles<\/strong><\/h3>\n\n\n\n

A central angle is twice<\/strong> the inscribed angle subtending the same arc.
\ud83d\udc49 \u2220Central = 2 \u00d7 \u2220Inscribed<\/strong><\/p>\n\n\n\n

\n\n\n\n

\ud83d\udfe4 Sector Area and Central Angle<\/strong><\/h3>\n\n\n\n

A sector is the slice of a circle<\/strong> formed by a central angle.
If \u03b8 is in degrees:
\ud83d\udcd8 Sector Area = (\u03b8\/360) \u00d7 \u03c0r\u00b2<\/strong><\/p>\n\n\n\n

\n\n\n\n

\ud83d\udd35 Real-Life Uses of Central Angles<\/strong><\/h3>\n\n\n\n

\ud83c\udf17 Clock angles
\ud83d\udcca Pie charts
\ud83c\udfa1 Ferris wheel rotations
\u2699\ufe0f Engineering and construction<\/p>\n\n\n\n

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

\n
\n

What is \u2220GFI ?<\/strong><\/p>\n\n\n

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

\u2220GFI = ______\u00b0<\/strong> <\/p>\n<\/div><\/div>\n\n\n\n

Look at the diagram:<\/p>\n\n\n

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

Write an equation showing that the measures of \u2220GFH,\u2220GFI and \u2220HFI sum to 360\u00b0, since they span an entire circle. Then solve for \u2220GFI.<\/p>\n\n\n\n

\u2220GFH + \u2220GFI + \u2220HFI = 360\u00b0<\/p>\n\n\n\n

150\u00b0 + \u2220GFI + 80\u00b0<\/strong> = 360\u00b0 Plug in <\/em>\u2220GFH = 150\u00b0 and <\/em> \u2220HFI = 80\u00b0<\/strong><\/p>\n\n\n\n

\u2220GFI + 230\u00b0 = 360\u00b0 Combine like terms<\/p>\n\n\n\n

\u2220GFI = 130\u00b0 Subtract 230\u00b0 from both sides<\/p>\n\n\n\n

So, \u2220GFI = 130\u00b0 <\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

What is \u2220RQS?<\/strong><\/p>\n\n\n

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

 \u2220RQS = _______\u00b0<\/strong> <\/p>\n<\/div><\/div>\n\n\n\n

Look at the diagram:<\/p>\n\n\n

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

Write an equation showing that the measures of \u2220RQS , \u2220RQT and \u2220SQT sum to 360\u00b0, since they span an entire circle. Then solve for \u2220RQS.<\/p>\n\n\n\n

\u2220RQS + \u2220RQT + \u2220SQT = 360\u00b0<\/p>\n\n\n\n

\u2220RQS+ 140\u00b0 + 120\u00b0<\/strong> = 360\u00b0 Plug in \u2220RQT = 140\u00b0 and <\/em> \u2220SQT = 120\u00b0<\/strong><\/p>\n\n\n\n

\u2220RQS + 260\u00b0 = 360\u00b0 Combine like terms<\/p>\n\n\n\n

\u2220RQS = 100\u00b0 Subtract 260\u00b0 from both sides<\/p>\n\n\n\n

So, \u2220RQS = 100\u00b0 <\/p>\n<\/div><\/div>\n\n\n\n

\n
\n

What is \u2220IHJ?<\/strong><\/p>\n\n\n

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

\u2220IHJ = _______\u00b0<\/p>\n<\/div><\/div>\n\n\n\n

Look at the diagram:<\/p>\n\n\n

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

Write an equation showing that the measures of \u2220IHK , \u2220JHK and \u2220IHJ sum to 360\u00b0, since they span an entire circle. Then solve for \u2220IHJ.<\/p>\n\n\n\n

\u2220IHK + \u2220JHK + \u2220IHJ= 360\u00b0<\/p>\n\n\n\n

140\u00b0 + 80\u00b0<\/strong> +\u2220IHJ = 360\u00b0 Plug in \u2220IHK = 140\u00b0 and <\/em> \u2220JHK  = 80\u00b0<\/strong><\/p>\n\n\n\n

\u2220IHJ + 220\u00b0 = 360\u00b0 Combine like terms<\/p>\n\n\n\n

\u2220IHJ = 140\u00b0 Subtract 220\u00b0 from both sides<\/p>\n\n\n\n

So, \u2220IHJ= 140\u00b0 <\/p>\n<\/div><\/div>\n\n\n\n

let’s practice!<\/p>\n\n\n\n

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

Central angles Key Notes : \ud83d\udd35 What is a Central Angle? A central angle is an angle whose vertex is at the center of a circle.Its rays (arms) point to the circumference of the circle.\u27a1\ufe0f Example: Angle \u2220AOB in circle O. \ud83d\udd34 Central Angle and Arc Measure A central angle cuts an arc on theContinue reading “L.2 Central angles”<\/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-196","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/196","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=196"}],"version-history":[{"count":16,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/196\/revisions"}],"predecessor-version":[{"id":18281,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/196\/revisions\/18281"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=196"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}