Question

in given figure O is the circle and angle BOC=120°find angle CDE

Answer 1

HEY MATE.....
HERE'S YOUR ANSWER

angle bac=60°
ABCD is a cyclic quadrilateral
(exterior angle of a cyclic quadrilateral is equal to its opposite interior angle)
angle cde= angle bac = 60°

Answer 2

therefore by theorem we know that
angle subtended by center of the circle at any part of the circle will be half the angle at the center
therefore.
BOC = 2 BAC
120=2BAC
BAC= 60

NOW as we know that ABCD is. a cyclic quadrilateral then opposite angles will make 180 degree together
therefore,

BAC + BDC= 180
60 + BDC= 180
BDC= 180-60
BDC = 120

THEREFORE
LINE BE
BDC+ CDE=180 (LINEAR PAIR)
120 + CDE=180
CDE= 180-120
CDE= 60

THEREFORE,

CDE = 60