Question

BC is a chord of a circle such that it subtends angle BAC and angle BDC in the same segment also angle BAC=69 and angle ABC=31 find the measure of angle BDC

Answer 1

In △ABC

∠BAC+∠ABC+∠ACB=180

o

(Angle sum property)

∠BAC+69

o

+31

o

=180

o

∠BAC=180

o

−100

o

=80

o

For segment BADCB,

VBDC and ∠BAC are angles in the same segment. So, they must be equal

∴ ∠BDC=∠BAC (Angles in the same segment are equal)

∠BDC=80

o

Hope it helps you...