Question

in the given figure if O is the centre of the circle angle abc equal to 30 degree and Angle C is equal to 140 degree find angle BOC.

Answer 1

Given : ABO=30°,COA=140°

To Find : BOC(reflex angle)

Construction : Extend AO To P

Proof :

IN ∆AOB
OA=OB(radii of the circle)
OBA=OAB(Angle opposite to equal sides are equal)
A+B+O=180°(A.S.P)
30°30°+O=180°
60°+O=180°
O=180°-60°
O=120°

AOB+BOP=180°(linear pair)
120°+BOO=180°
BOP=180°-120°
BOP=60°

AOC+COP=180°
140+COP=180°
COP=180°-140°
COP=40°

BOP+COP=BOC
60°+40°=100°

=BOC=100°

Answer 2

angle AOC is an exterior angle for triangle BOA.
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