Question

In the given figure, arc AB = twice arc BC and ∠AOB = 80°. Find :
(i) ∠BOC
(ii) ∠OAC

Answer 1

Answer:

∠BOC=40° and ∠OAC=30°

Step-by-step explanation:

Given arc AB=twice arc BC and ∠AOB = 80°. We have to find the ∠BOC and ∠OAC.

Let the arc BC be x and also radius r

As,

∴ Arc AB=2x

⇒ x=r/2×2/9

Put this value in above equation, we get

⇒ 360/9 =40°

Hence, ∠BOC=40°

∠AOC=80°+40°=120°

Now, by angle sum property in ΔAOC

∠AOC+∠OAC+∠OCA=180°

⇒ 120°+2∠OAC=180°

⇒ ∠OAC=30°