Question

In given figure AOC is a diameter of the circle and arc AXB = 1/2 arc BYC. Then, angle BOC is equal to

Answer 1

Angle BOC = 120°.

Step-by-step explanation:

Given:

In given figure, AOC is a diameter of the circle

arc AXB = $\frac{1}{2}\times$arc BYC

We know that, central angle is always equal to its opposite arc  

Therefore ∠AOB = $\frac{1}{2}\times$ ∠BOC  (1)

Also,  ∠ AOB + ∠BOC =  180° [linear pair  axiom]

$\frac{1}{2}\times \angle BOC + \angle BOC = 180\°$     [from equation 1]

$\frac{\angle BOC +2 \angle BOC}{2}=180\°$

$\frac{3 \angle BOC}{2} =180\°$

∠BOC = $\frac{180\times2}{3}$

∠BOC  = $\frac{360}{3}$

Hence  ∠BOC = 120°.

Answer 2

Answer:

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