o is the centre of circle,reflex<aob=260.c is the point of minor arc ab of the circle .find<acb
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Construction::
Draw angle AOB and Angle ACB
Given that AB is minor arc and Angle ACB is equal to x and AOB = y.
As per theorem of angle subtended by an arc at centre is twice the angle it subtends at circumference (any point)
Angle 2x = 360-y
So x = 180-y/2 (1)
IF ACBO is a parallelogram then angle x = angle y (opp angles are eual)
Also from (1) x= 180-y/2
Solving the equation we get 360=3y So y = 120 and x=y so x= 120 degree.
Draw angle AOB and Angle ACB
Given that AB is minor arc and Angle ACB is equal to x and AOB = y.
As per theorem of angle subtended by an arc at centre is twice the angle it subtends at circumference (any point)
Angle 2x = 360-y
So x = 180-y/2 (1)
IF ACBO is a parallelogram then angle x = angle y (opp angles are eual)
Also from (1) x= 180-y/2
Solving the equation we get 360=3y So y = 120 and x=y so x= 120 degree.
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Answer:
We know, the angle at the center of a circle is twice the angle at the circumference subtended by the same arc. Hence,
∠ACB=21×reflex(∠AOB)
=2260
=130∘
Step-by-step explanation:
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