ABCD is a cyclic quadrilateral. AB is produced to E. It is given that angle DAC=20degree and angle ACD=65degree. Find angle ODC and angle CBE
Answers
Given : ABCD is a cyclic quadrilateral. AB is produced to E ∠DAC= 20° , ∠ACD = 65°
To Find : ∠ODC & ∠CBE
Solution:
in ΔACD
∠DAC + ∠ACD + ∠ADC = 180°
=> 20° + 65° + ∠ADC = 180°
=> ∠ADC = 95°
∠ADC + ∠ABC = 180° ( sum of opposite angle of cyclic quadrilateral)
=> 95° + ∠ABC = 180°
=> ∠ABC =85°
∠ABC + ∠CBE = 180°
=> ∠CBE = 95°
∠DOC= 2∠DAC ( angle by chord CD at center and arc segment)
=> ∠DOC= 2 * 20°
=> ∠DOC= 40°
in ΔDOC
OD = OC ( radius)
=> ∠ODC = ∠OCD
∠ODC + ∠OCD + ∠DOC = 180°
=> 2∠ODC + 40° = 180°
=> ∠ODC = 70°
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