# In the adjoining figure, AOB is a straight line. Find the value of x.

Question:

In the adjoining figure, AOB is a straight line. Find the value of x. Also, find ∠AOC, ∠COD and ∠BOD.

Solution:

AOB is a straight line. Therefore,

$\angle A O C+\angle C O D+\angle B O D=180^{\circ}$

$\Rightarrow(3 x+7)^{\circ}+(2 x-19)^{\circ}+x^{\circ}=180^{\circ}$

$\Rightarrow 6 x=192^{\circ}$

$\Rightarrow x=32^{\circ}$

Therefore,

$\angle A O C=3 \times 32^{\circ}+7=103^{\circ}$

$\angle C O D=2 \times 32^{\circ}-19=45^{\circ}$ and

$\angle B O D=32^{\circ}$