Question

In the circle with the centre O,Ac is the diameter .Angle AOB is 80 degree and ACE is 10 degree find the value of angle BED

Answer 1

Answer:

Step-by-step explanation

join bc

ange boc=100

(Angle at the centre is double the angle at the circumference subtended by the same chord)

angle bec=50=angle dce (altt inerior angle)

angle eac=120

angle oab=60

anglebcd=10 +50+40=100

herfore  angkle bed= 180-100=80

Answer 2

∠BOC=180

∘

−80

∘

=100

∘

⇒∠BEC=50

∘

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Angle subtended by arc at centre is double as that of at the circumference.

[alternateangles]

∠BOC+∠OCB+∠OBC

[∠OCB=∠OBC]

∵OC=OB

⇒∠OCB=40

∘

⇒∠ECD=50

∘

∠OCB=40

∘

∠BCD=50

∘

+40

∘

+10

∘

∠BCD=100

∘

∠BCD+∠DEB=180

∘

∠DEB=80

∘

∠DEC=30

∘

∠CED=30

∘

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