Question

In the given figure, arc AB = twice arc BC and AOB = 80o . 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, $\text{Length of arc=}x=r\times \frac{\angle BOC}{360}$

∴ Arc AB=2x

$\text{Length of arc=}=2x=r\times \frac{80}{360}$

⇒ $x=\frac{r}{2}\times \frac{2}{9}$

Put this value in above equation, we get

$\frac{r}{2}\times \frac{2}{9}=r\times \frac{\angle BOC}{360}$

⇒ $\angleBOC=\frac{360}{9}=40^{\circ}$

Hence, ∠BOC=40°

∠AOC=80°+40°=120°

Now, by angle sum property in ΔAOC

∠AOC+∠OAC+∠OCA=180°

⇒ 120°+2∠OAC=180°

⇒ ∠OAC=30°

Answer 2

Here is the solution