Question

Find the measure of arc ADC if angle OAB=30° and angle OCB=50°

Answer 1

in triangle AOB,
 OB=OA (radii of circle)
this implies, angle OAB=angle OBA= 30 degree

Similarly in triangle OBC,
angle OCB=angleOBC=50 degree

also, angle (OBA+OBC)=angleABC
Hence, angle OBC=80 degree

Also, angle 2OBC= angle AOC

hence, angle AOC= 160

length of arc= 160/360 .2pi(radius)

then u can calculate.

but what is the radius.

Answer 2

Answer:

OB=OA (Radii of same circle) SO,

angle OAB= angle OBA=30...........(i)

Similarly

OB=OC(Radii of same circle)

angle OCB= angle OBC=50..........(ii)

Adding both (i) and ( ii)

angle OBA +angle OBC=50+30

angle ABC = 80

we know that angle subtented by an arc at center is double of at remaining part os circle

so,

1. angle AOC=2 angle ABC
2. angle AOC=160

HOPE ITS HELP ALL OF YOU ALL ............................

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