Question

In a figure angle AOB : angle BOC = 2 : 3. If angle AOC = 75 degree then find the measure of angle AOB and angle BOC ?

Answer 1

Let, ∠AOB=2x and ∠BOC=3x
∠AOC=∠AOB+∠BOC=75°
or, 2x+3x=75°
or, 5x=75°
or, x=15°
∴, ∠AOB=2×15°=30° and
∠BOC=3×15°=45°

Answer 2

Therefore, The value of $\angle AOB$ and $\angle BOC$ are $114$° and $171$°

Step-by-step explanation:

Given,

$\angle AOB:\angle BOC=2:3$ and $\angle AOC=75$°

From figure,

We know,

Angle around a point is equal to $360$°

∴$\angle AOB+\angle BOC+\angle AOC=360$

⇒$\angle AOB+\angle BOC=360-75$

⇒$\angle AOB+\angle BOC=285$

Let,

$\angle AOB=2x$ and $\angle BOC=3x$ (∵$\angle AOB:\angle BOC=2:3$)

∴$2x+3x=285$

⇒$5x=285$

⇒$x=\frac{285}{5}$

⇒$x=57$

∴$\angle AOB=(2\times 57)=114$° and $\angle BOC=(3\times 57)=171$°

So, The value of $\angle AOB$ and $\angle BOC$ are $114$° and $171$°