Question

O is the centre of circle and angle AOC = 120 degree and angle ABC is

Answer 1

Given :-

• O is the centre of a circle and $\rm\angle{AOC = 120^{\circ}}$

To Find:-

• The Value of $\rm\angle{ABC}$

Construction :-

• Connect AP and CP

Theorem used:-

• Angle subtended by an arc at the center of the circle is twice the angle angle subtended bt it in any point.

• Sum of either Pair of opposite angle of cyclic Quadrilateral is 180°

Now,

→ $\rm{\dfrac{1}{2}\times{\angle{AOC}} = \angle{APC}}$

→ $\rm{\dfrac{1}{2}\times{120} = \angle{APC}}$

→ $\rm{\angle{APC} = 60^{\circ}}$

But, APCB is a Cyclic Quadrilateral

Therefore,

→ $\rm{\angle{ABC} + \angle{APC} = 180}$

→ $\rm{\angle{ABC} + 60^{\circ} = 180^{\circ}}$

→ $\rm{\angle{ABC} = 180 - 60 }$

→ $\rm{\angle{ABC} = 120^{\circ}}$

Hence, The value of ABC is 120°.

Answer 2

Answer:

Angle ABC is 120 degree

Step-by-step explanation:

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