Question

2) In the figure, O is the centre of the circle, such that mL AOC = 140° then find / ABC?​

Answer 1

Answer:

Correct option is

B

72∘

From the figure, if we draw a straight line from A to C, we get line AC which is a chord of the circle .

Angle subtended by any chord at the centre of a circle is 

double than that of the angle subtended by that chord at any point on circumference of the circle.

∴∠AOC = 2.∠ABC

So ∠AOC = 72∘

therefore option B will be the answer.

Answer 2

∠ADC$\frac{1}{2}$ ∠AOC =($\frac{1}{4}$ ×140°) = 70°

∠ABC+∠ADC = 180°

∠ABC + 70° = 180°

∠ABC = 180° - 70° =180°

∠ABC = 110°

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