Question

In the diagram, $\overrightarrow{\mathrm{OB}}$bisects $\angle \mathbf{AOC}$and $\overleftrightarrow{\mathrm{EC}}\perp \overleftrightarrow{\mathrm{OD}}$.

Find the value of x.

m∠2 = 6x + 9, m∠5 = 2x + 49

Short answer

The value of x is 10.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is :

Step 2. Write the relation between the angles ∠2 and ∠5.

From the given diagram it can be noticed that the angles∠2and∠5are the vertical angles.

Therefore, by using the theorem for vertical angles it can be said that the angles∠2and∠5have the same measure.

That implies, $m\angle 2=m\angle 5$.

Therefore, the relation between the angles ∠2 and ∠5 is $m\angle 2=m\angle 5$.

Step 3. Find the value of x.

As, m∠2 =m∠5, m∠2 =6x + 9 andm∠5 = 2x + 49.

Therefore, the value of x is given by :

$m\angle 2=m\angle 5$

$6x+9=2x+49$

$6x-2x=49-9$

$4x=40$

$x=\frac{40}{4}$

$x=10$

Therefore, the value of x is 10.