Question

in fig.find the measure of the arcADC if angle OAB=30 &OCB=50

Answer 1

given: a circle in which angle OAB=30° and angle OCB=50°.

to find: measure of arc ADC or angle subtended by arc ADC.

solution: let D be a point on the circle between A and C.

now, in ∆AOB since,
OA=OB (radius of same circle)
so angle OBA=30° (angle opposite equal sides are equal)

similarly,
in ∆COB since,
OB=OC (radius of same circle)
so angle OBC=50° (angle opposite equal sides are equal)

so, angle OBA+OBC=30°+50°=80°
therefore, angle ABC=80°

so, angle AOC or arc ADC=80×2=160°
(angle subtended by an arc at the center is double tge abgle subtended by the same arc at any point of the circle)

hope it helped you.
plz let me know if it is wrong.

Answer 2

AngleAOC=160*(by theorem)