Question

ABC is inscribed in a circle center O if AOB =140 and BOC = 100 find ABC

Answer 1

Step-by-step explanation:

We know that

AOC+COB+AOB =360°

100+140+AOC=360°

AOC=120___________________________(360-240)

ABC is half of AOC by DEGREE MEASURE THEOREM

So

ABC=120/2=60°

HOPE IT HELPS AND PLZ MARK IT AS BRAINLIEST

Answer 2

∠ABC = 60°

Step-by-step explanation:

Given:

Here ABC is inscribed in a circle with center O.

∠AOB = 140° and ∠BOC = 100°

Now,

S shown in the figure below, we have

∠AOB + ∠BOC + ∠AOC = 360°

140° + 100° + ∠AOC  = 360°

240° + ∠ AOC  = 360°

∠AOC = 360° - 240°

∠AOC = 120°                       [1]

Also, angle subtended by an chord at the centre is double that of the angle subtend by the same chord at any point of circle.

Let us assume chord AC

∠AOC = 2 ∠ABC

$\angle ABC= \frac{AOC}{2}$

$\angle ABC = \frac{120}{2}$

∠ ABC = 60°