31. AB and CD are equal arcs of a circle with centre O.
(i) If angle AOB = 130°, find angle ODC.
(ii) If angle OCD = 60°, find angle AOB.
Answers
AnsweR :
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Answer:
(i)IfangleAOB=130°,findangleODC.
\sf \: In \: \triangle \: AOB \: and \: \triangle \: ODC.In△AOBand△ODC.
\sf OA = OB = OD = OC = radiusOA=OB=OD=OC=radius
\sf \angle \: AOB \: = \: \angle\: DOC\: = 130 \degree∠AOB=∠DOC=130°
\sf \: In \: \triangle \: ODCIn△ODC
\sf OC = ODOC=OD
\sf \angle \: OCD \: = \angle \: ODC∠OCD=∠ODC
\sf \angle \: ODC + \angle \: OCD + \angle \: DOC = 180 \degree∠ODC+∠OCD+∠DOC=180°
\sf2 \angle \:ODC = 180 \degree - 130 \degree2∠ODC=180°−130°
\sf \angle \: ODC = 50 \degree = \angle \: OCD∠ODC=50°=∠OCD
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\sf( \: ii \: ) \: If \: angle \: OCD \: = \: 60°, \: find \: angle \: AOB.(ii)IfangleOCD=60°,findangleAOB.
\sf AB = CDAB=CD
\sf \angle \: AOB = \angle \: COD∠AOB=∠COD
\sf In \: \triangle \: CODIn△COD
\sf \: OC = OD = radiusOC=OD=radius
\sf \angle \: ODC \: = \angle \: OCD \: = 60 \degree∠ODC=∠OCD=60°
\sf \angle \: COD \: = 60 \degree \: [ by \: angle \: sum \: property]∠COD=60°[byanglesumproperty]
\sf \angle \: AOB = \angle \: COD = 60 \degree∠AOB=∠COD=60°