c.
In the given diagram, AC is the diameter of the circle,
with centre 0. CD and BE are parallel.
LAOB - 80 and angle LACE -10. Find:
© BEC,
(11) BCD.
(iii) CED.
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∠BEC = 50° , ∠BCD = 100° , ∠CED = 30°
Step-by-step explanation:
AC is Diamter and O is center
=> AOC is straight line
=> ∠BOC = 180° - ∠AOB
=> ∠BOC = 180° - 80°
=> ∠BOC = 100°
∠BEC = ∠BOC/2 ( angle by same chord BC at center & arc segment)
=> ∠BEC = 100°/2
=> ∠BEC = 50°
CD ║ BE
=> ∠DCE = ∠BEC = 50°
∠BCA = ∠AOB/2
=> ∠BCA = 80°/2
=> ∠BCA = 40°
∠BCD = ∠BCA + ∠ACE + ∠DCE
=> ∠BCD = 40° + 10° + 50°
=> ∠BCD = 100°
∠BCD + ∠BED = 180° ( opposite angle of cyclic quadrilateral)
=> ∠BED = 80°
∠BED = ∠BEC + ∠CED
=> 80° = 50° + ∠CED
=> ∠CED = 30°
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