{"id":11329,"date":"2022-07-07T19:36:08","date_gmt":"2022-07-07T14:06:08","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11329"},"modified":"2022-07-07T19:36:13","modified_gmt":"2022-07-07T14:06:13","slug":"in-the-figure-triangle-odc-triangle-oba-angle-boc-125-and-angle-cdo-70-find-the-angle-doc-angle-dco-and-angle-oab","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/in-the-figure-triangle-odc-triangle-oba-angle-boc-125-and-angle-cdo-70-find-the-angle-doc-angle-dco-and-angle-oab\/","title":{"rendered":"In the figure, \\(\\triangle\\) ODC ~ \\(\\triangle\\) OBA, \\(\\angle\\) BOC = 125 and \\(\\angle\\) CDO = 70. Find the \\(\\angle\\) DOC, \\(\\angle\\) DCO and \\(\\angle\\) OAB."},"content":{"rendered":"
Since BD is a line and OC is a ray on it.<\/p>\n
\\(\\angle\\) DOC + \\(\\angle\\) BOC = 180<\/p>\n
So,\u00a0 \\(\\angle\\) DOC + 125 = 180<\/p>\n
\\(\\angle\\) DOC = 55<\/p>\n
In triangle CDO, we have :<\/p>\n
\\(\\angle\\) CDO + \\(\\angle\\) DOC + \\(\\angle\\) DCO = 180<\/p>\n
70 + 55 + \\(\\angle\\) DCO = 180<\/p>\n
\\(\\angle\\) DCO = 55<\/p>\n
Given that \\(\\triangle\\) ODC ~ \\(\\triangle\\) OBA<\/p>\n
\\(\\angle\\) ODC = \\(\\angle\\) OBA, \\(\\angle\\) OCD = \\(\\angle\\) OAB<\/p>\n
\\(\\angle\\) OBA = 70 and \\(\\angle\\) OAB = 55<\/p>\n
Hence, \\(\\angle\\) DOC = 55, \\(\\angle\\) DCO = 55 and \\(\\angle\\) OAB = 55\u00a0<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":" Solution : Since BD is a line and OC is a ray on it. \\(\\angle\\) DOC + \\(\\angle\\) BOC = 180 So,\u00a0 \\(\\angle\\) DOC + 125 = 180 \\(\\angle\\) DOC = 55 In triangle CDO, we have : \\(\\angle\\) CDO + \\(\\angle\\) DOC + \\(\\angle\\) DCO = 180 70 + 55 + \\(\\angle\\) DCO = …<\/p>\n