Question

‘O’ is the centre of the circle . Angle D= 80degree.
Find the following:

(a) Angle C
(b) Angle ABC
(c) Angle BAC
(d) Angle F

Answer 1

Given : O’ is the center of the circle . Angle D= 80degree.

To Find :  (a) Angle C

(b) Angle ABC

(c) Angle BAC

(d) Angle F

Solution:

Angle C  and Angle D , both are  in same sector by same arc AB

Hence ∠C = ∠D = 80°

O is center hence AOC is diameter

=> ∠ABC  = 90°

in ΔABC

∠ABC + ∠C +  ∠BAC  = 180°

=> 90° +  80° + ∠BAC  = 180°

=>  ∠BAC  = 10°

∠D + ∠F  = 180°    as AFBD is cyclic Quadrilateral

Hence 80° + ∠F  = 180°

=> ∠F  = 100°

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